The two squares and the shaded region of square A is in the attachment.
Answer: The shaded region of A is 12.5% of the area of B.
Step-by-step explanation: Assume that the length of side of square A is a and the length of side of square B is b.
Length a is half (50%) of length b:
a = [tex]\frac{b}{2}[/tex]
The shaded region is a triangle. The area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
b and h are the sides of the square A, so:
[tex]A_{1}[/tex] = [tex]\frac{\frac{b}{2}.\frac{b}{2}}{2}[/tex]
[tex]A_{1} = \frac{b}{2}.\frac{b}{2}.\frac{1}{2}[/tex]
[tex]A_{1} = \frac{b^{2}}{8}[/tex]
Area of square B is:
[tex]A_{2}[/tex] = b.b
[tex]A_{2} = b^{2}[/tex]
Comparing areas:
[tex]\frac{\frac{b^{2}}{8} }{b^{2}}[/tex] = [tex]\frac{b^{2}}{8}.\frac{1}{b^{2}}[/tex] = [tex]\frac{1}{8}[/tex]
As percentage:
[tex]\frac{1}{8}[/tex] × 100 = 0.125 × 100 = 12.5%
Comparing the shaded region of A to square B, the area of the first is 12.5% smaller than the second.
