Question

The area of a square is 64cm2 find the area of square formed by joining the midpoint of the given square.

Answer 1

area of square = 64cm²

Now we have to join it's mid points .

area = (side)² = 64

side = 8cm

In ∆ABD ,

P is midpoint of AB

Q is mid point of AD

By mid point theorem ,

PQ = 1/2 DB ,. ------(1)

in ∆ ADB ,

by Pythagoras theorem ,

AD² + AB² = BD²

8² + 8² = BD²

64+64 = BD²

128 = BD²

BD = √128 Or 8√2

now substituting value of BD in eq 1,

PQ = 1/2BD

PQ = 1/2 × 8√2

PQ = 4√2

we got a side of sq. PQRS ,

Now area of PQRS = (side)²

=> (4√2)²

=> 32 cm²