Find the area of the shaded portion if the side of the square measures 20 cm?

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Find the area of the shaded portion if the side of the square measures 20 cm (use Pi = 3.14)

posted Jun 16, 2015

Consider R as the radius of each circle. Divide the figure in 4 quarters.
In any quarter: the blue area is a quarter of disc (pi*R²/4) from which we remove a blank part, which is the small square size R² minus the same quarter of disc. So this petal has an area of (pi*R²/4 - (R² - pi*R²/4)) = R² (2*pi/4 - 1) = R²/4 (2*pi - 4)
Now for the 4 petals, multiply by four: A = R² (2*pi - 4)

For a big square of side 20 cm, R=10 cm thus area is 100*(2*pi - 4) = (200*pi - 400) cm², around 228,32 cm²
228 cm² if you take pi=3,14

–1 vote

4 semi circles=square + the shaded area
or two circles = square + the shaded area
therefore shaded area =(2 circles - square )= (2*3.14*100-400)=228 sq cm

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