Question

The length of the diagonal of a square is 16 centimetre find its area and perimeter

Answer 1

area of square, if diagonal is given

=1/2(d square)

=1/2(16*16)

= 128

perimeter of square, if diagonal is given

= 2* root 2 *d

=2·2·16.

≈45.2

Answer 2

solution:-

• we know the all angles of square are of 90°

• all side of square are equal and diagonals are equal.

so,

let, diagonal is hypotenuse

now, by Pythagoras theorem

S = side.

=> (1st S)²+(2cd S)² =(Hypotenuse)²

=> x² + x² = (16)²

=> 2x = 16

=> x = 16/2

=> x = 8

length of sides of square are 8 cm.

=> Area of square = (side) × (side)

=> Area of square = 8 × 8

=> Area of square = 64 cm².

√=> perimeter of square = 4×(side)

√=> perimeter of square = 4 × 8

√=> perimeter of square = 32 cm

8 cm , 64 cm² and 32cm are length of side , area and perimeter of the square respectively.

i hope it helps you.