Question

The area of square ABCD is 16 cm². Find the area of square joining the mid roints of the sides.​

Answer 1

Answer:

The diagonal length= √(4²+4²)= 4√2cm. The area of the small square = 2√2 × 2√2 =4×2= 8cm²

Answer 2

Answer:

The area of square ABCD is 16 cm². The area of squares joining the mid points of the sides is 8cm².

Step-by-step explanation:

Given: The area of square ABCD is 16 cm².

Find the area of squares joining the midpoints of the sides.​

Find the length of the side of the square by using its area.

The area of square = (side)²

(side)² = 16

The length of the side of a square= √16=4 cm

The diagonal length= √(4²+4²)= 4√2cm.

By midpoint theorem, the side made by joining the midpoints of the square = 1/2 of diagonal

Therefore side of small square = 4√2 /2 = 2√2cm

The area of the small square = 2√2 × 2√2 =4×2= 8cm².