Answer:
12.5%
Step-by-step Explanation:
==>Given:
Square A side length = 50% Square B side length
Area of Square A that is shaded = ½ of the area of Square B
==>Required:
Area of shaded region of Square A as a % of Area of Square B
==>Solution:
Let "b" be the side length of Square B
Let "a" be the side length of Square A
Since we are told that the side length of Square A (a) = 50% of side length of Square B (b), thus we have,
a = ½b
==>Let's find the area of Square A and Square B:
Area of a square = s², where s = side length
Area of Square A = (½b)² = b²/4
Area of Square B = b²
==>Let's find the area of the shaded region of the Square A = ½ of area of Square A.
Thus,
Area of shaded region of Square A = ½*(b²/4) = b²/8
==>Let's express the area of the shaded portion of square A as a percentage of are of Square B:
Thus, Area of shaded portion of Square A ÷ Area of Square B × 100%
[tex] = \frac{\frac{b^{2} }{8} }{b^{2} } * 100 [/tex]
[tex] = \frac{b^{2} }{8} * \frac{1}{b^{2} } * 100 [/tex]
[tex] = \frac{b^{2}*1 }{8*b^{2} } * 100 [/tex]
[tex] = \frac{b^{2} }{8*b^{2} } * 100 [/tex]
[tex] = \frac{1}{8} * 100 = 12.5 [/tex]
The area of the shaded region of Square A is 12.5% of the area of Square B.
