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Find the area of the shaded region use 3.14 as necessary

Find the area of the shaded region use 3.14 as necessary-example-1
User Bernardo Mendes
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1 Answer

18 votes
18 votes

From the information given,

A is the center of the circle

AB is the radius

AB = 5

BC is the diameter of the circle

BC = 2 x radius = 2 x 5 = 10

Area of shaded region = Area of circle - area of triangle

The formula for calculating the area of a circle is

Area = πr^2

where

r is the radius of the circle

Area of circle = 3.14 x 5^2 = 78.5

Triangle BAD is congruent to triangle CAD

Thus, BD = CD

Triangle BDC is a right triangle

We would apply the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

hypotenuse = BC = 10

one leg = other leg = BD = CD

Thus,

10^2 = BD^2 + CD^2 = 2BD^2

100 = 2BD^2

BD^2 = 100/2 = 50

BD = √50

BD = 5√2

The formula for calculating the area of a triangle is

Area = 1/2 x base x height

height = 5√2

base = 5√2

Area = 1/2 x 5√2 x 5√2 = 1/2 x (5√2)^2

Area of triangle = 25

Area of shaded region = 78.5 - 25

Area of shaded region = 53.5 cm^2

User James Webster
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2.9k points