Question

9. If the diagonal of a square is 12 centimeters, the area of the square is

A. 102 cm2.
B. 36 cm2.
C. 144 cm2.
D. 72 cm2.

Answer 1

36 cm2.

Explanation:

The area of square A is 324 cm2. Since the dimensions of square A are three times larger than the dimensions of square B, the scale factor is 3.

To find the area of square B, first square the scale factor, 3.

3 squired =9

Next, divide the area of square A by 9.

324÷ cm2 ÷ 9 =36 cm2

Answer 2

D. 72 cm²

Explanation:

The area of a square is given by ;

Area= l² where l = length

Given that the diagonal is 12 cm, let assume length of the square to be l

Apply the Pythagorean relationship where a=b=l

l² + l² = 12²

2 l² = 144

l²= 144/2

l²= 72

l =√72 =8.485 cm

⇒length of the square= l= 8.485 cm

⇒Area of the square= l² = 8.485² = 72 cm²