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Pop55

Answer:

36.5cm²

Step-by-step explanation:

Area of quarter circle=8²[tex]\pi[/tex]/4=64[tex]\pi[/tex]/4=16[tex]\pi[/tex]cm²

Area of square+Area of shaded region =2(16[tex]\pi[/tex])=32[tex]\pi[/tex]=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.

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jcherry99

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

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