Question

The area of a square ABCD is 64 sq. cm. Find the area of square obtained by joining the mid-points of
the sides of the square ABCD.​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

❖ Area of square ABCD = 64 sq. cm

⇛ AB² = 64

⇛ AB = 8 cm

❖ Let P, Q, R , S be the midpoints of the sides of square AB, BC, CD, DA respectively.

⇛BP = 4 cm and BQ = 4 cm

❖ In ∆PBQ, ∠B=90°

❖ By pythagoras theorem,

❖ PQ² = PB² + BQ²

⇛ PQ² = 4² + 4²

⇛ PQ² = 16 + 16

⇛ PQ² = 32

⇛ PQ = √(32)

⇛PQ = √(2×2×2×2×2)

⇛ PQ = 4 √2 cm

❖So, Area of square PQRS = PQ² = (4√2)² = 32 sq. cm

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