Question

The diagonal of a square is 12 cm; find its area and length of one side
Apply (phthygorous theorm​

Answer 1

Answer:

72 cm² is the area and length of one side is 6√2 cm

Step-by-step explanation:

Area of a square with diagonal

= 1/2 × d²

= 1/2 × 12 × 12

= 6 × 12

= 72 cm²

Length of one side = √72

= √36 × √2

= 6√2 cm

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 = (12)²

=> 2x = 12

=> x = 12/2

=> x = 6

length of sides of square are 8 cm.

=> Area of square = (side) × (side)

=> Area of square = 6 × 6

=> Area of square = 36 cm².

√=> perimeter of square = 4×(side)

√=> perimeter of square = 4 × 6

√=> perimeter of square = 24 cm

6 cm , 36 cm² and 24cm are length of side , area and perimeter of the square respectively.

i hope it helps you.