Question

what happens to the area of a square of its side is a)halved b) doubled

Answer 1

heya!!

what happens to the area of a square of its side is

a) halved

Answer -

area = side x side

So, if the side is halved, then -

new area
= side / 2 x side / 2
= side x side / 4
= area / 4

Hence, the area becomes the quarter of what it was before.

b) doubled

Area = side × side ( x × x = x² )

So, if the side is doubled, then -

new area
= 2x × 2x = 4x²

So, doubling the side length multiplies the area by 4.

#hope it helps!!

Answer 2

Given:

• Sides of a square: 1. half   2. Double

To Find:

• The area of a square when its length of the side is halved.
• The area of a square when its length of the side is doubled.

Solution:

We already know that,

Area of a square = side×side = $side^2$

Let 'x' be the value of the length of the side of a square.

⇒ Area = $x^2$

1. When the length of the side of a square is half.

⇒ Area = $(\frac{1}{2}x)^2$

⇒ Area = $\frac{1}{4}x^2$

⇒ Area = $\frac{x^2}{4}$

2. When the length of the side of a square is doubled.

⇒ Area = $(2x)^2$

⇒ Area = $4x^2$

∴ 1. When the length of the side of a square is half, area = $\frac{x^2}{4}$

2. When the length of the side of a square is doubled, area = $4x^2$