Question

The diagonal of a square is 12 cm long. Find its area and perimeter.​

Answer 1

Answer:

Area of square = 1/2 (d)²

= 1/2 (12)²

= 1/2 × 12 × 12

= 72 cm sq

Side of a square = √Area

= √72

= √(2 × 2 × 2 × 3 × 3)  

= 2 × 3√2

= 6 × 1.41

= 8.46 cm

Perimeter of square = 4 × 8.46 = 33.84 cm

Answer 2

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Diagonal AC=BD= 12 cm

Let each side of the square ABCD is x cm.Then,

Using the formula,

Area of square is x²cm²

In right triangle ABC,

AB²+BC²=AC²

=>x²+x²=12²

=>2x²=144cm²

=>x²=72cm

Hence, area of square is 72cm².

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