In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square....

Question

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm^2, is:

A. 12.50
B. 6.25
C. 3.125
D. 1.5625

Accepted Answer

Area of the smallest shaded square = 25/8 = 3.125 cm^2 A large square has side 5 cm (area 25 cm^2). Each successive inner square is formed by joining the midpoints of the outer square's sides. Each time you do this, the new square's area is exactly half the previous square's area. Four nested squares are shown; the smallest (third inner square, fourth overall) is shaded.

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm^2, is: A. 12.50 B. 6.25 C. 3.125 D. 1.5625