Question

The area of a square is 64square cm. Find the area of th square formed by joining midpoints of the given square

Answer 1

Given, area of the square = 64 sq. cm
If each side of the square is a,
Area of square = a²
a² = 64
a = 8 cm

Since it joins the midpoint of the sides of the square (a1), the side of the new square formed, by Pythagoras theorem is,

a1² = 4² + 4²
a1² = 16+16
a1² = 32
a1 = 4√2

Therefore area of the new square = a1² = 4√2 × 4√2
= 32 (Ans.)