Mensuration in 6th-grade math deals with measuring the areas and perimeters of various shapes. Here’s a summary of the key concepts:

**1. Units of Measurement:**

- We use standard units like centimeters (cm), meters (m), and millimeters (mm) to measure length.

**2. Area:**

- Area represents the amount of space a flat surface occupies.
- We measure area in square units (cm², m², etc.).
- Formulas are used to calculate the area of different shapes:
- Square: Area = side × side
- Rectangle: Area = length × breadth

**3. Perimeter:**

- Perimeter is the total length of all sides of a closed figure.
- We measure perimeter in linear units (cm, m, etc.).
- Formulas are used to calculate the perimeter of different shapes:
- Square: Perimeter = 4 × side
- Rectangle: Perimeter = 2 × (length + breadth)

**4. Applications:**

- Mensuration helps solve real-life problems like finding the amount of cloth needed for a dress (area) or the length of fencing required for a garden (perimeter).

Here are some additional points to consider:

**Understanding Shapes:**It’s important for students to recognize basic shapes like squares, rectangles, and triangles.**Visualization:**Drawing diagrams can help students visualize shapes and understand the concepts better.**Practice:**Solving practice problems helps students solidify their understanding of formulas and apply them to various scenarios.

By grasping these concepts, students develop a foundation for understanding geometry and measurement in higher grades.

**Exercise 10.1**

**1. Find the perimeter of each of the following figures:**

**Ans : **

(a) The required perimeter is: 4 cm + 2 cm + 1 cm + 5 cm = 12 cm

(b) The required perimeter is: 40 cm + 35 cm + 23 cm + 35 cm = 133 cm or 1.33 m

(c) The required perimeter is: 15 cm + 15 cm + 15 cm + 15 cm = 15 cm x 4 = 60 cm

(d) The required perimeter is: 4 cm + 4 cm + 4 cm + 4 cm + 4 cm – 4 cm x 5 = 20 cm

(e) The required perimeter is: 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm + 1 cm = 15 cm

(f) The required perimeter is: 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm = 52 cm

**2. The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?**

**Ans : **

**Identify the sides:**The lid is a rectangle with a length of 40 cm and a breadth of 10 cm (given in the problem).**Perimeter formula for rectangle:**Perimeter of a rectangle = 2 (Length + Breadth)**Calculation:**- Perimeter = 2 (40 cm + 10 cm)
- Perimeter = 2 x 50 cm
- Perimeter = 100 cm

Therefore, 100 cm of tape is required to seal the lid of the rectangular box all around.

**3. A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?**

**Ans : **

**Convert centimeters to meters for consistency:**- Length = 2 m 25 cm = 2 m + (25 cm / 100 cm/m) = 2.25 m
- Breadth = 1 m 50 cm = 1 m + (50 cm / 100 cm/m) = 1.50 m

**Perimeter formula for rectangle:**Perimeter of a rectangle = 2 (Length + Breadth)**Calculation:**- Perimeter = 2 (2.25 m + 1.50 m)
- Perimeter = 2 x 3.75 m
- Perimeter = 7.50 m

Therefore, the perimeter of the table-top is 7.50 meters.

**4. What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?**

**Ans : **

**Identify the sides:**The photograph is a rectangle with a length of 32 cm and a breadth of 21 cm.**Perimeter formula for rectangle:**Perimeter of a rectangle = 2 (Length + Breadth)**Calculation:**- Perimeter = 2 (32 cm + 21 cm)
- Perimeter = 2 x 53 cm
- Perimeter = 106 cm

Therefore, 106 cm of wooden strip is required to frame the photograph.

**5. A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?**

**Ans : **

**Convert kilometers to meters for perimeter calculation:**- Length (m) = 0.7 km * 1000 m/km = 700 m
- Breadth (m) = 0.5 km * 1000 m/km = 500 m

**Calculate the perimeter of the land:**The perimeter represents the total length of the fence required. Perimeter = 2 (Length + Breadth) Perimeter = 2 (700 m + 500 m) Perimeter = 2 * 1200 m Perimeter = 2400 m**Account for four rows of wires:**Since each side needs to be fenced with 4 rows of wires, we multiply the perimeter by 4. Total wire length = Perimeter × Number of wire rows Total wire length = 2400 m * 4**Calculate the total length of wire needed:**Total wire length = 9600 meters

Therefore, 9600 meters of wire are needed to fence the rectangular piece of land with 4 rows of wires on each side.

**6. Find the perimeter of each of the following shapes:**

**(a) A triangle of sides 3 cm, 4 cm and 5 cm.**

**(b) An equilateral triangle of side 9 cm.**

**(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.**

**Ans :**

**(a) Triangle with sides 3 cm, 4 cm and 5 cm:**

Perimeter = Side 1 + Side 2 + Side 3 Perimeter = 3 cm + 4 cm + 5 cm Perimeter = 12 cm

**(b) Equilateral Triangle with side 9 cm:**

An equilateral triangle has all three sides equal.

Perimeter = Side 1 + Side 2 + Side 3 (all sides are 9 cm) Perimeter = 9 cm + 9 cm + 9 cm Perimeter = 27 cm

**(c) Isosceles Triangle with equal sides 8 cm and third side 6 cm:**

An isosceles triangle has two sides with the same length.

Perimeter = Side 1 + Side 2 + Side 3 Perimeter = 8 cm + 8 cm + 6 cm Perimeter = 22 cm

**Therefore:**

- The perimeter of the triangle in (a) is 12 cm.
- The perimeter of the equilateral triangle in (b) is 27 cm.
- The perimeter of the isosceles triangle in (c) is 22 cm.

**7. Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.**

**Ans : **To find the perimeter of a triangle, we simply add the lengths of all its sides. Here’s how to find the perimeter of the triangle with sides 10 cm, 14 cm, and 15 cm:

**Perimeter = Side 1 + Side 2 + Side 3**

**Perimeter = 10 cm + 14 cm + 15 cm**

**Perimeter = 39 cm**

Therefore, the perimeter of the triangle is 39cm

**8. Find the perimeter of a regular hexagon with each side measuring 8 m.**

**Ans : **

**Identify the number of sides:**A hexagon has 6 sides.**Perimeter formula for regular shapes:**Perimeter of a regular polygon = Number of sides × Side length**Calculation:**- Perimeter = 6 sides × 8 meters/side
- Perimeter = 48 meters

Therefore, the perimeter of the regular hexagon is 48 meters.

**9. Find the side of the square whose perimeter is 20 m.**

**Ans : **

**Perimeter Formula for Square:**Perimeter of a square = 4 × Side length**Given Information:**We know the perimeter of the square is 20 meters.**Solve for Side Length:**- Since the perimeter is 20 meters, we can set up the equation: 20 m = 4 × Side length
- To find the side length, we need to isolate it. Divide both sides of the equation by 4: (20 m) / 4 = (4 × Side length) / 4

**Side Length:**- Simplifying the equation, we get: 5 m = Side length

Therefore, the side of the square is 5 meters.

**10. The perimeter of a regular pentagon is 100 cm. How long is its each side?**

**Ans : **

- Perimeter = Number of sides × Side length Perimeter = 5 × s
**Given Information:**We know the perimeter of the pentagon is 100 cm.**Solve for Side Length (s):**- Set up the equation based on the given information: 100 cm = 5 × s
- To find the side length (s), isolate it by dividing both sides by 5: (100 cm) / 5 = (5 × s) / 5

**Side Length (s):**- Simplify the equation: 20 cm = s

Therefore, each side of the regular pentagon is 20 centimeters long.

**11. A piece of string is 30 cm long. What will be the length of each side if the string is used to form:**

**(a) a square?**

**(b) an equilateral triangle?**

**(c) a regular hexagon?**

**Ans : **

(a) **Square:**

- In a square, all sides are equal in length.
- Perimeter of the square = Length of the string (given as 30 cm)
- Let the side of the square be ‘s’ cm.
- Perimeter = 4 × s (formula for square’s perimeter)
- Substitute the known value: 30 cm = 4 × s

**Solving for s (side of the square):**

- Divide both sides by 4: 30 cm / 4 = (4 × s) / 4
- Simplify: s = 7.5 cm

Therefore, each side of the square would be 7.5 cm long.

(b) **Equilateral Triangle:**

- In an equilateral triangle, all sides are equal in length.
- Perimeter of the equilateral triangle = Length of the string (30 cm)
- Let the side of the triangle be ‘s’ cm.
- Perimeter = 3 × s (formula for equilateral triangle’s perimeter)
- Substitute the known value: 30 cm = 3 × s

**Solving for s (side of the equilateral triangle):**

- Divide both sides by 3: 30 cm / 3 = (3 × s) / 3
- Simplify: s = 10 cm

Therefore, each side of the equilateral triangle would be 10 cm long.

(c) **Regular Hexagon:**

- In a regular hexagon, all sides are equal in length.
- Perimeter of the regular hexagon = Length of the string (30 cm)
- Let the side of the hexagon be ‘s’ cm.
- Perimeter = 6 × s (formula for regular hexagon’s perimeter)
- Substitute the known value: 30 cm = 6 × s

**Solving for s (side of the regular hexagon):**

- Divide both sides by 6: 30 cm / 6 = (6 × s) / 6
- Simplify: s = 5 cm

Therefore, each side of the regular hexagon would be 5 cm long.

In summary:

- Square: Each side = 7.5 cm
- Equilateral Triangle: Each side = 10 cm
- Regular Hexagon: Each side = 5 cm

**12. Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?**

**Ans : **

**Identify the given information:**- Two sides of the triangle: 12 cm and 14 cm
- Perimeter of the triangle: 36 cm

**Set up the equation:**- Let the third side of the triangle be “x” cm.
- Perimeter = Side 1 + Side 2 + Side 3
- Substitute the known values: 36 cm = 12 cm + 14 cm + x cm

**Solve for x (third side):**- Combine the known side lengths: 36 cm = 26 cm + x cm
- To isolate x, subtract the combined known side lengths from both sides: 36 cm – 26 cm = (26 cm + x cm) – 26 cm
- Simplify: 10 cm = x cm

Therefore, the third side of the triangle is 10 centimeters long.

**13. Find the cost of fencing a square park of side 250 m at the rate of? 20 per metre.**

**Ans : **

**Calculate the perimeter of the square park:**- A square has all sides equal.
- Perimeter of a square = 4 × Side length (given as 250 m)
- Perimeter = 4 × 250 m = 1000 m

**Identify the rate per meter:**- The cost per meter of fencing is 20 per metre (given).

**Calculate the total cost of fencing:**- Total cost = Perimeter × Rate per meter
- Total cost = 1000 m × 20 per metre = 20000

Therefore, the cost of fencing the square park is ₹20,000.

**14. Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of ₹12 per metre.**

**Ans : **

**Calculate the perimeter of the park:**- A rectangle’s perimeter is the total length of all its sides added together.
- Perimeter = 2 (Length + Breadth)
- Given: Length (l) = 175 m and Breadth (b) = 125 m
- Perimeter = 2 (175 m + 125 m)
- Perimeter = 2 x 300 m
- Perimeter = 600 m

**Identify the rate per meter:**- The cost per meter of fencing is ₹12 (given).

**Calculate the total cost of fencing:**- Total cost = Perimeter × Rate per meter
- Total cost = 600 m × ₹12 per meter
- Total cost = ₹7200

Therefore, the cost of fencing the rectangular park is ₹7200.

**15 . Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?**

**Ans : **

**Calculate the distance covered by Sweety (square park):**

- Perimeter of a square = 4 × Side length
- Side length of Sweety’s park (square) = 75 m (given)
- Perimeter of Sweety’s park = 4 × 75 m = 300 m

**Calculate the distance covered by Bulbul (rectangular park):**

- Perimeter of a rectangle = 2 (Length + Breadth)
- Length of Bulbul’s park = 60 m (given)
- Breadth of Bulbul’s park = 45 m (given)
- Perimeter of Bulbul’s park = 2 (60 m + 45 m) = 2 × 105 m = 210 m

**Comparison:**

- Sweety’s park perimeter (distance covered) = 300 m
- Bulbul’s park perimeter (distance covered) = 210 m

**Conclusion:**

Bulbul covers less distance (210 m) compared to Sweety (300 m).

**16. What is the perimeter of each of the following figures? What do you infer from the answers?**

**Ans : **

(a) The perimeter of the square is calculated as: 25 cm + 25 cm + 25 cm + 25 cm = 4 x 25 cm = 100 cm

(b) The perimeter of the rectangle is calculated as: 30 cm + 20 cm + 30 cm + 20 cm = 2 x (30 cm + 20 cm) = 2 x 50 cm = 100 cm

(c) The perimeter of the rectangle is calculated as: 40 cm + 10 cm + 40 cm + 10 cm = 2 x (40 cm + 10 cm) = 2 x 50 cm = 100 cm

(d) The perimeter of the triangle is the sum of all sides: 30 cm + 30 cm + 40 cm = 100 cm

From the above answers, we conclude that different shapes can have equal perimeters.

**17. Avneet buys 9 square paving slabs, each with a side of 1/7 m. He lays them in the form of a square.**

**(a) What is the perimeter of his arrangement [Fig. (i)]?**

**(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [Fig. (ii)]?**

**(c) Which has greater perimeter?**

**(d) Avneet wonders, if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges, i.e., they can not be broken).**

**Ans : **

(a) The arrangement is in the form of a square of side

(b) Perimeter of cross-arrangement

(c) Since 10 m > 6 m

∴ Cross-arrangement has greater perimeter.

(d) Total number of tiles = 9

∴ We have the following arrangement

The above arrangement will also have the greater perimeter.

**Exercise 10.2**

Find the areas of the following figures by counting square:

**Ans : **

**(a)** Number of full squares = 9

Area of 1 square = 1 sq unit

∴ Area of 9 squares = 9 x 1 sq unit = 9 sq units

So, the area of the portion covered by 9 squares = 9 sq units

**(b)** Number of full squares = 5

∴ Area of the figure = 5 x 1 sq unit = 5 sq units

**(c)** Number of full squares = 2

Number of half squares = 4

∴ Area of the covered figure = 2 x 1 + 4 x 1/2 = 2 + 2 = 4 sq units

**(d)** Number of full squares = 8

∴ Area of the covered portion of the figure = 8 x 1 sq unit = 8 sq units

**(e)** Number of full squares = 10

Area covered by the figure = 10 x 1 sq unit = 10 sq units

**(f) **Number of full squares = 2 Number of half squares = 4 ∴ Area of the covered figure = (2 x 1 + 4 x 1/2) = (2 + 2) sq units = 4 sq units

**(g) **Number of full squares = 4

Number of half squares = 4

∴ Area of the covered figure = (4 x 1 + 4 x 1/2) = (4 + 2) sq units = 6 sq units

**(h)** Number of full squares = 5

∴ Area of the covered figure = 5 x 1 sq unit = 5 sq units

**(i)** Number of full squares = 9

∴ Area of the covered figure = 9 x 1 sq unit = 9 sq units

**(j) **Number of full squares = 2

Number of half squares = 4

∴ Area of the covered figure = (2 x 1 + 4 x 1/2) sq units = (2 + 2) sq units = 4 sq units

**(k)** Number of full squares = 4 Number of half squares = 2 ∴ Area of the covered figure = (4 x 1 + 2 x 1/2) sq units = (4 + 1) sq units = 5 sq units

**(l)** Number of full squares = 4

Number of squares more than half = 3

Number of half squares = 2

∴ Area of the covered figure = (4 x 1 + 3 x 1 + 2 x 1/2) sq units = (4 + 3 + 1) sq units = 8 sq units

**(m) **Number of full squares = 6

Number of more than half squares = 8

Area of the covered figure = (6 x 1 + 8 x 1) sq units = (6 + 8) sq units = 14 sq units

**(n)** Number of full squares = 9

Number of more than half squares = 9

∴ Area of the covered figure = (9 x 1 + 9 x 1) sq units = (9 + 9) sq units = 18 sq units

**Exercise 10.3**

**1. Find the areas of the rectangles whose sides are:**

**(a) 3 cm and 4 cm**

**(b) 12 m and 21 m**

**(c) 2 km and 3 km**

**(d) 2 m and 70 cm**

**Ans : **

(a) **Sides: 3 cm and 4 cm** Area = 3 cm × 4 cm = 12 cm²

(b) **Sides: 12 m and 21 m** Area = 12 m × 21 m = 252 m²

(c) **Sides: 2 km and 3 km (convert kilometers to meters for consistency)** 1 km = 1000 m Area = 2 km × 3 km = (2 × 1000 m) × (3 × 1000 m) = 6,000,000 m²

(d) **Sides: 2 m and 70 cm (convert centimeters to meters for consistency)** 100 cm = 1 m Area = 2 m × (70 cm / 100 cm/m) = 2 m × 0.7 m = 1.4 m²

**2. Find the areas of the squares whose sides are:**

**(a) 10 cm**

**(b) 14 cm**

**(c) 5 m**

**Ans : **

**Area of a square = Side length × Side length**

(a) **Side: 10 cm**

Area = 10 cm × 10 cm = 100 cm²

(b) **Side: 14 cm**

Area = 14 cm × 14 cm = 196 cm²

(c) **Side: 5 m**

Area = 5 m × 5 m = 25 m²

**3. The length and breadth of three rectangles are as given below:**

**(a) 9 m and 6 m**

**(b) 17 m and 3 m**

**(c) 4 m and 14 m**

**Ans : **

**Area = Length × Breadth**

**Finding the Area for Each Rectangle:**

Now, let’s find the area of each rectangle using the given information:

(a) **Length = 9 m, Breadth = 6 m**

Area = 9 m × 6 m = 54 square meters (m²)

(b) **Length = 17 m, Breadth = 3 m**

Area = 17 m × 3 m = 51 square meters (m²)

(c) **Length = 4 m, Breadth = 14 m**

Area = 4 m × 14 m = 56 square meters (m²)

**4. The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.**

**Ans : **

- Length of the garden (l) = 50 meters (given)
- Area of the garden (A) = 300 square meters (given)

**Understand the relationship between area and dimensions of a rectangle:**The area of a rectangle is the product of its length and width. We can express this with the formula: A = l × b (where A is area, l is length, and b is width)**Solve for the width (b):**- We need to isolate the width (b) in the formula.
- Since we know the length (l) and the area (A), we can rearrange the formula to solve for b: b = A / l

**Calculate the width (b):**- Substitute the known values: b = 300 m² / 50 m b = 6 meters

Therefore, the width of the rectangular garden is 6 meters.

**5. What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹8 per hundred sq m?**

**Ans : **

**Calculate the area of the plot:**- Area of a rectangle = Length × Breadth
- Length (l) = 500 m (given)
- Breadth (b) = 200 m (given)
- Area = 500 m × 200 m = 100,000 square meters (sq m)

**Understand the rate per unit area:**- The rate is given as ₹8 per hundred sq m. This means the cost applies to every 100 sq m of the plot.

**Calculate the total cost:**- We need to find out how many times the cost of ₹8 applies to the entire area (100,000 sq m).
- Divide the total area by the area covered by the given rate: Number of times the rate applies = 100,000 sq m / 100 sq m/unit = 1000 units
- Multiply the number of units by the cost per unit to find the total cost: Total cost = Number of units × Cost per unit Total cost = 1000 units × ₹8/unit = ₹8000

Therefore, the cost of tiling the rectangular plot of land is ₹8000.

**6. A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?**

**Ans : **

- We know the width is 1 meter and 50 centimeters (1 m 50 cm).
- 1 centimeter (cm) is equal to 0.01 meters (m).
- Width in meters = 1 m + (50 cm * 0.01 m/cm)
- Width in meters = 1 m + 0.5 m
- Width in meters = 1.5 m

**Calculate the area:**

- Area of a rectangle = Length × Breadth
- Length (l) = 2 meters (given)
- Breadth (b) = 1.5 meters (calculated)
- Area = 2 m × 1.5 m = 3 square meters (m²)

Therefore, the area of the table-top is 3 square meters.

**7. A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?**

**Ans : **

- The width is given as 3 meters and 50 centimeters (3 m 50 cm).
- We know 1 centimeter (cm) is equal to 0.01 meters (m).
- Width in meters = 3 m + (50 cm * 0.01 m/cm)
- Width in meters = 3 m + 0.5 m
- Width in meters = 3.5 meters

**Calculate the room’s area:**

- Area of a rectangle = Length × Breadth
- Length (l) = 4 meters (given)
- Breadth (b) = 3.5 meters (calculated)
- Area = 4 m × 3.5 m = 14 square meters (m²)

Therefore, you will need 14 square meters of carpet to cover the floor of the room.

**8. A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.**

**Ans : **

**Calculate the area of the floor:**- Area of a rectangle = Length × Breadth
- Length of the floor (l) = 5 meters (given)
- Breadth of the floor (b) = 4 meters (given)
- Area of the floor = 5 m × 4 m = 20 square meters (m²)

**Calculate the area of the square carpet:**- Area of a square = Side length × Side length
- Side length of the carpet (s) = 3 meters (given)
- Area of the carpet = 3 m × 3 m = 9 square meters (m²)

**Area of the non-carpeted floor:**- The non-carpeted area is the difference between the total floor area and the carpeted area.
- Area of non-carpeted floor = Area of the floor – Area of the carpet
- Area of non-carpeted floor = 20 m² – 9 m² = 11 square meters (m²)

Therefore, the area of the floor that is not carpeted is 11 square meters.

**9. Five square flower beds each of side 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?**

**Ans : **

**Calculate the area of one flower bed:**- Area of a square = Side length × Side length
- Side length of a flower bed (s) = 1 meter (given)
- Area of one flower bed = 1 m × 1 m = 1 square meter (m²)

**Calculate the total area of the five flower beds:**- Number of flower beds = 5 (given)
- Total area of flower beds = Number of flower beds × Area of one flower bed
- Total area of flower beds = 5 × 1 m² = 5 square meters (m²)

**Calculate the area of the whole piece of land:**- Area of the land = Length × Breadth
- Length of the land (l) = 5 meters (given)
- Breadth of the land (b) = 4 meters (given)
- Area of the land = 5 m × 4 m = 20 square meters (m²)

**Calculate the area of the remaining land:**- The remaining land is the difference between the total land area and the total area occupied by the flower beds.
- Area of remaining land = Area of the land – Total area of flower beds
- Area of remaining land = 20 m² – 5 m² = 15 square meters (m²)

Therefore, the area of the remaining part of the land is 15 square meters.

**10. By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).**

**Ans : **

**Figure (a):**

**Splitting into rectangles:**- The figure can be split into two rectangles: Rectangle I and Rectangle II.
- Rectangle I has dimensions 3 cm × 4 cm (from the image).
- Rectangle II has dimensions 4 cm × 3 cm (from the image).

**Calculating the area of each rectangle:**- Area of Rectangle I = 3 cm × 4 cm = 12 cm²
- Area of Rectangle II = 4 cm × 3 cm = 12 cm²

**Calculating the total area of the figure:**- The total area is the sum of the areas of both rectangles.
- Total area of figure (a) = Area of Rectangle I + Area of Rectangle II
- Total area of figure (a) = 12 cm² + 12 cm² = 24 cm²

**Figure (b):**

**Splitting into rectangles:**- The figure can be split into three rectangles: Rectangle I, Rectangle II, and Rectangle III (all with the same dimensions).
- Each rectangle has dimensions 3 cm × 1 cm (from the image).

**Calculating the area of each rectangle:**- Area of each rectangle = 3 cm × 1 cm = 3 cm²

**Calculating the total area of the figure:**- The total area is the sum of the areas of all three rectangles.
- Total area of figure (b) = 3 cm² + 3 cm² + 3 cm² = 9 cm²

**11. Split the following shapes into rectangles and find their areas (The measures are given in centimetres).**

**Ans : **

**(a) **By splitting the given figure into rectangles I and II, we get:

Area of rectangle I: = 12 cm x 2 cm = 24 sq cm

Area of rectangle II: = 8 cm x 2 cm = 16 sq cm

∴ The total area of the whole figure is: 24 sq cm + 16 sq cm = 40 sq cm.

**(b)** By splitting the given figure into rectangles I, II, and III, we get:

Area of rectangle I: = 7 cm x 7 cm = 49 sq cm

Area of rectangle II: = 21 cm x 7 cm = 147 sq cm

Area of rectangle III: = 7 cm x 7 cm = 49 sq cm

∴ The total area of the whole figure is: 49 sq cm + 147 sq cm + 49 sq cm = 245 sq cm.

**12. How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively:**

**(a) 100 cm and 144 cm**

**(b) 70 cm and 36 cm**

**Ans : **

**1. Calculate the area of one tile:**

- Area of a tile = Length × Breadth
- Tile length = 12 cm (given)
- Tile breadth = 5 cm (given)
- Area of one tile = 12 cm × 5 cm = 60 cm²

**2. Find the area of the rectangular region for each case:**

(a) **Length = 100 cm, Breadth = 144 cm:**

- Area of the region = Length × Breadth
- Area = 100 cm × 144 cm = 14400 cm²

(b) **Length = 70 cm, Breadth = 36 cm:**

- Area of the region = Length × Breadth
- Area = 70 cm × 36 cm = 2520 cm²

**3. Calculate the number of tiles required for each case:**

(a) Number of tiles for region (a) = Area of region (a) / Area of one tile

- Number of tiles = 14400 cm² / 60 cm² = 240 tiles

(b) Number of tiles for region (b) = Area of region (b) / Area of one tile

- Number of tiles = 2520 cm² / 60 cm² = 42 tiles