Question

Calculate the shaded area of the figure.

Answer 1

Answer:

36.5cm²

Step-by-step 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

Answer:

Area shaded area = 36.48

Step-by-step 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