Question

How can i solve this question?​

Answer 1

`PQ=4√(2) \:cm=5.66 \: cm`

Area of square PQRS
`= 32\: cm^2`

Explanation:

ABCD is a square. Points P, Q, R and S are the midpoints of sides AB, BC, CD and DA of square ABCD respectively.

Therefore,

BP = 1/2 * AB = 1/2 *8 = 4 cm

BQ = 1/2 * BC = 1/2 *8 = 4 cm

In
`\triangle PBQ, \: m\angle PBQ =90\degree`

Therefore, by Pythagoras theorem:

`PQ=√(4^2 +4^2)`

`PQ=√(2*4^2)`

`PQ=4√(2) \:cm=5.66 \: cm`

Area of square PQRS
`=PQ^2`

Area of square PQRS
`=(4√(2)) ^2`

Area of square PQRS
`= 32\: cm^2`