Semicircles, Not Circles

Geometry Level 1

Given a square of side length 2, we draw semicircles on opposite sides.

What is the area of the yellow region?

π − 3 \pi - 3 π 3 \frac{\pi}{3} 4 − π 4 - \pi 1 1

Chung Kevin by Chung Kevin , 46, Australia

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2 solutions

Nikhil Raj
Jun 7, 2017

There are two semicircle of same radius. Both will combine to make a full circle of radius 1. Area of circle = π r 2 = π area of square = a 2 = 2 2 = 4 Area of yellow region = Area of square − Area of circle = 4 − π {\text{Area of circle}} = \pi r^2 = \pi \\ {\text{area of square}} =a^2 = 2^2 = 4 \\ \boxed{{\text{Area of yellow region}} = {\text{Area of square}} - {\text{Area of circle}} = 4 - \pi}

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area yellow region = area of square - area of circle = 2^2 - pi x 1^2 = 4 - pi

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Rearranging the areas help :)

Chung Kevin - 4 years, 7 months ago

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