Question

Calculate the shaded area of the figure.

Answer 1

36.5cm²

Explanation:

Area of quarter circle=8²
`\pi`/4=64
`\pi`/4=16
`\pi`cm²

Area of square+Area of shaded region =2(16
`\pi`)=32
`\pi`=100.5cm²

Area of square=8²=64cm²

Area of shaded region=100.5cm²-64cm²=36.5cm²

Therefore, the area of the shaded region is 36.5cm².

Answer 2

Area shaded area = 36.48

Explanation:

Preliminary

• Draw a line from D to B
• Assume that the quarter circle has its center at C.
• Find the area of the quarter circle. [Arc DBC]
• Subtract the area of TriangleDBC
• That 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 cm
• 4 sides of the square = 32 cm
• The center of the quarter circle is at C

Solution

Quarter Circle Area

Formula

Area = 1/4 * pi * r^2

Solution

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

Triangle Area

Formula

Area = 1/2 r^2

Given

r = 8

Solution

• Area = 1/2 8^2
• Area = 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 = 50.24
• Area of triangle= 32

Solution

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

Area Shaded area = 36.48