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

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1 Answer
sankarankalyanam
Nov 28, 2017

Area of the shaded portion #= r^2#

Explanation:

Circumference of the whole circle = #2pir#
Circumference of the curved portion of the shaded area #= 2r#
Ratio of circumferences #= (2r)/(2pir )= 1/pi#

Areas of shaded region and the whole circle will be in the proportion #(1/pi)#

Area of the whole circle #= pi r^2#

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

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