How can i solve this question?

Question

asked Apr 3, 2022 128k views

1 Answer

Luke Taylor · Answer 1 · 2022-04-07T23:49:21+0000

Answer:

$PQ=4√(2) \:cm=5.66 \: cm$

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
$= 32\: cm^2$