Question

6)Calculate the area of a square whose diagonals are 20 cm long

Answer 1

Answer:

200 cm

Step-by-step explanation:

length of diagonal= 20 cm

side of square =

${a}$

formula of diagonal=

$a \sqrt{2}$

derivation

$a\sqrt{2} = 20 \\ a \sqrt{2} = 10 \times \sqrt{4} \\ a = 10 \times \sqrt{2}$

area of square=

${a}^{2}$

derivation of area of square=

${a}^{2} = ({10 \times \sqrt{2}) \ }^{2} \\ {a}^{2} = 100 \times 2 \\ {a}^{2} = 200$

So, area of square is equal to 200 cm