In the figure above quadrilateral ABCD is a square of side 50M. Points P, Q, R, S are midpoints of side AB, BC, CD, AD respectively. Find the are of shaded region
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The area of shaded portion is 535.7 sq. M.
Given,
ABCD is a square of side 50M.
Points P, Q, R, S are midpoints of side AB, BC, CD, AD.
Area of shaded portion = Area of sqaure - 4 × Area of quadrants.
= a^2 - 4 × π×r^2/4
a = 50 M
r = a/2 = 50/2 =25 M
Area of shaded portion
= a^2 - 4 × π×r^2/4
= a^2 - 4 × π×(a/2)^2/4
= 50^2 - 4 × 22/7 × 25^2/4
= 2500 - 4 × 22/7 × 625/4
= 2500 - 13750/7
= 535.7 sq. M
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