Calculate the shaded area of the figure.

Area shaded area = 36.48

Step-by-step explanation:

Preliminary

Draw a line from D to BAssume that the quarter circle has its center at C. Find the area of  the quarter circle. [Arc DBC]Subtract the area of TriangleDBCThat gives 1/2 the shaded area. Double the 1/2 of the shaded area

Given

ABCD is a square. It better be or we can't do this.One side of the square = 8 cm4 sides of the square =   32 cmThe center of the quarter circle is at C

Solution

Quarter Circle Area

Formula

Area = 1/4 * pi * r^2

Solution

r = 8 cmpi = 3.14Area = 1/4 * 3.14 * 8^2Area = 50.24 cm^2

Triangle Area

Formula

Area = 1/2 r^2

Given

r = 8

Solution

Area = 1/2 8^2Area = 32 cm^2

Area of 1/2 the Shaded area

Formula

Area of 1/2 shaded area = Area of 1/4 circle - Area of Triangle

Givens

Area of 1/4 circle = 50.24Area of triangle= 32

Solution

Area of 1/2 shaded area = 50.24 - 32Area of 1/2 shaded area = 18.24Answer= 2* 18.24

Area Shaded area = 36.48

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