A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 11. Mensuration

Subject: Maths - Class 8^th

Q. No. 1 of Exercises 11.1

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1

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Let breadth of the rectangle be b

∵ Perimeter of the rectangle = Perimeter of the square

∴ 2 × (80 + b) = 4 × 60

⇒ b = 40 m

Now, area of square = a² = 60² = 3600 m²

And area of the rectangle = lb = 80 × 40 = 3200 m²

Clearly, area of square is greater.

2

Chapter Exercises

Exercises 11.1

Exercises 11.2

Exercises 11.3

Exercises 11.4

1

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

2

Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

3

The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 – (3.5 + 3.5) metres].

4

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m²? (If required you can split the tiles in whatever way you want to fill up the corners).

5

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression C = 2πr, where r is the radius of the circle.

A. B.

C.