Area of Rectangle Questions

Area of rectangle questions with solutions are given here for practice. A rectangle is a quadrilateral whose opposite sides are equal, and all angles are equal to 90 degrees.

Learn more about the properties of rectangles.

Video Lesson on Properties of Rectangles

Click here to learn more about how to calculate the area of rectangle.

Area of Rectangle Questions with Solutions

Now that we have learnt about the properties and area of rectangles, let us solve a few questions.

Question 1:

Calculate the area of a rectangle whose length is 28 cm and width is 34 cm.

Solution:

Length of the rectangle = 28 cm

Width of the rectangle = 34 cm

Area of the rectangle = 28 × 34 = 952 cm².

Question 2:

Calculate the area of a rectangle whose length is 30 m and width is 1200 cm.

Solution:

Length of the rectangle = 30 m

Width of the rectangle = 1200 cm = 12 m

Area of the rectangle = 30 × 12 = 360 m².

Question 3:

Calculate the area and length of the diagonal of a rectangle whose perimeter is 46 cm and length is one less than twice the width.

Solution:

Let the width of the rectangle be x, and then the length of the rectangle will be 2x – 1.

Now, the perimeter of the rectangle = 2 × (L + B) = 46 cm

⇒ 2 × (2x – 1 + x) = 46

⇒ 3x – 1 = 46 ÷ 2

⇒ 3x = 23 + 1

⇒ x = 24/3 = 8

∴ length of the rectangle = 2x – 1 = 2(8) – 1 = 15 cm

Width of the rectangle = x = 8 cm

Diagonal of the rectangle = √(Length² + Width²)

= √(15² + 8²) = √(225 + 64) = √289

= 17 cm

Area of the rectangle = 15 × 8 = 120 cm².

Question 4:

Calculate the length and breadth of the rectangle whose area is 512 cm² and the length is twice the breadth.

Solution:

Let the breadth of the rectangle be x, and then the length will be 2x.

Area of rectangle = x × 2x = 512

⇒ 2x² = 512

⇒ x² = 512/2 = 256

⇒ x² = 256

⇒ x = 16

Thus, the breadth is 16 cm, and the length is 32 cm.

Question 5:

A wire is bent into a circle of radius 20 cm, then it is again bent into a rectangle of width 8 cm. Find the area of the rectangle formed.

Solution:

Since the same wire is bent into a circle and a rectangle,

The circumference of the circle = Perimeter of the rectangle

Radius of the circle = 20 cm.

The circumference of the circle = 2𝜋r = 2 × 3.14 × 20 = 125.6 cm

Width of rectangle = 8 cm

Perimeter of rectangle = 2 (Length + 8) = 125.6

⇒ Length = (125.6 ÷ 2) – 8 = 54.8 cm

∴ the area of the rectangle = 54.8 × 8 = 438.4 cm².

Question 6:

How many small rectangles of length 8 cm and width of 6 cm are needed to make a square of area 576 cm²?

Solution:

Area of each small rectangle = 8 × 6 = 48 cm²

Number of small rectangles needed = Area of square ÷ area of a small rectangle

= 576 ÷ 48 = 12

∴ 12 such rectangles are needed.

Question 7:

Find the area of the rectangle whose width is 4 cm and the length of the diagonal is 5 cm.

Solution:

Width of the rectangle = 4 cm.

Diagonal of the rectangle = 5 cm

Area of the rectangle = Width (Diagonal^2. – Width²)^1/2 = 4 × (5² – 4²)^1/2

= 4 × 3 = 12 cm².

Also Read:

• Area and Perimeter of Different Shapes
• Surface Areas and Volume of Shapes
• Area of Rectangle Calculator

Question 8:

Find the area of the rectangle whose length is 21 cm and the length of the diagonal is 29 cm.

Solution:

Length of the rectangle = 21 cm

Diagonal of the rectangle = 29 cm

Area of the rectangle = Length (Diagonal^2. – Length²)^1/2 = 21 × (29² – 21²)^½

= 21 × (841 – 441)^1/2

= 21 × 20 = 420 cm².

Question 9:

Find the cost of painting 4 walls of dimensions 12 m × 3 m, if the cost of painting per square metre is ₹ 5.

Solution:

Area of a wall = 12 × 3 = 36 m²

Area of 4 walls = 4 × 36 = 144 m²

Cost of painting per square metre = ₹ 5

Cost of painting 144 m² = 144 × 5 = ₹ 720.

∴ The cost of painting 4 walls of the given dimension is ₹ 720.

Question 10:

A rectangular park of length 30 m and breadth 25 m has a path of uniform width 5 m around its perimeter. Find the cost of tiling the whole path if the cost of tiling per 10 m² is ₹ 1500.

Solution:

Length of the park = 30 m

Breadth of the park = 25 m

Area of park = 30 × 25 = 750 m²

Area of the park and path = 40 × 35 = 1400 m²

Required area of the path = Area of shaded portion = Area of the park and path – area of the park

= 1400 – 750 = 650 m².

Cost of tiling per 10 m² = ₹ 1500

Cost of tiling 1 m² = ₹ 150

Cost of tiling 650 m² = 650 × 150 = ₹ 97,500.

∴ The cost of tiling the path is ₹ 97,500.

Question 11:

The floor of a room has to be covered with square tiles 30 cm each. If the length and the breadth of the room are 22.5 m and 10 m, respectively, find how many tiles are required to cover the whole floor.

Solution:

Length of the room = 22.5 m = 22.5 × 100 cm = 2250 cm

Breadth of the room = 10 m = 10 × 100 cm = 1000 cm

Area of the room = 2250 × 1000 = 22,50,000 cm²

Area of one tile = 30 × 30 = 900 cm²

Number of tiles = Area of room ÷ area of one tile = 22,50,000 ÷ 900 = 2500

∴ 2500 tiles are needed to cover the whole floor.

Question 12:

The perimeter of a square of side 25 cm is equal to the perimeter of a rectangle whose width is 2/5th the side of the square. Find the area of the rectangle.

Solution:

Side of square = 25 cm

Perimeter of square = 4 × 25 = 100 cm

Width of the rectangle = ⅖ of 25 cm = ⅖ × 25 = 10 cm

Let x be the length of the rectangle. Given that the perimeter of the square is equal to the perimeter of the rectangle.

∴ Perimeter of rectangle = 2 × (x + 10) = 100 cm

⇒ x = 100/2 – 10 = 40 cm

Area of the rectangle = 40 × 10 = 400 cm²

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Practice Questions on Area of Rectangle

1. Complete the following table:

2. A rectangular park of length 45 m and breadth 15 m has a path of uniform width 2.5 m around its perimeter. Find the cost of tiling the whole path if the cost of tiling per 20 m² is ₹ 1800.

3. How many small squares of length 26 cm are needed to make a rectangle whose length is 7.8 m and breadth is 3.9 m?

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