in the figure given above abcd is a square of side 50 points P Q R S are midpoint of side ab side bc side cd side ad respectively find area of shaded region
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Answer:537.5
Step-by-step explanation:find area of the square.find area of a sector multiply by 4 . subtract from the area of square
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The area of shaded region is 535.7 sq. points.
Given,
ABCD is a square of side 50 points.
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 points
r = a/2 = 50/2 =25 points
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. points
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