How do you find the area of the shaded region in the diagram below?

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How do you find the area of the shaded region in the diagram below?

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Answer 1 · 2017-11-28T13:04:19

Area of the shaded portion $= r^{2}$ $= r^2$

Explanation:

Circumference of the whole circle = $2 π r$ $2pir$
Circumference of the curved portion of the shaded area $= 2 r$ $= 2r$
Ratio of circumferences $= \frac{2 r}{2 π r} = \frac{1}{π}$ $= (2r)/(2pir )= 1/pi$

Areas of shaded region and the whole circle will be in the proportion $(\frac{1}{π})$ $(1/pi)$

Area of the whole circle $= π r^{2}$ $= pi r^2$

$:.$ Area of the shaded portion
= $(cancel(pi )r^2) /cancel (pi) = r^2$

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How do you find the area of the shaded region in the diagram below?

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