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Worksheet: Area of Composite Shapes: Polygons and Sectors

Q1:

Find the area of the shaded part in this figure. Round your answer to the nearest tenth.

Q2:

Find the area of the shape below using 2 2 7 as an approximation for 𝜋 . Round your answer to two decimal places.

Q3:

Using 3.14 to approximate 𝜋 , find the area of the shaded region.

Q4:

In rectangle 𝐴 𝐵 𝐶 𝐷 , a circle is removed that touches both sides 𝐴 𝐵 and 𝐷 𝐶 . Using 3.14 to approximate 𝜋 , what is the area of the remaining piece?

Q5:

Find the area of the following figure to the nearest tenth.

Q6:

The diagram below shows a circle of radius 𝑟 cm inscribed in a triangle of base 7 𝑦 cm and height 3 𝑥 cm. Find an expression for the area, in cm2, of the shaded region given that the area of a circle is given by 𝐴 = 𝜋 𝑟 2 . What is the degree of your area expression?

  • A The expression = 2 1 2 𝑦 𝑥 , and it is of the second degree.
  • B The expression = 2 1 𝑦 𝑥 𝜋 𝑟 2 , and it is of the first degree.
  • C The expression = 2 1 𝑦 𝑥 , and it is of the first degree.
  • D The expression = 2 1 2 𝑦 𝑥 𝜋 𝑟 2 , and it is of the second degree.

Q7:

Using the approximation 2 2 7 for 𝜋 , calculate the area of the shaded part.

Q8:

Find the area of the shaded region, using 2 2 7 to approximate 𝜋 .

Q9:

Using 3.14 as an approximation for 𝜋 , find the area of the shaded part.

Q10:

Using 3.14 as an approximation for , find the area of the shaded shape.

Q11:

Find the area of this shape. (You may use 2 2 7 to approximate 𝜋 .)

Q12:

Using 3.14 as an estimate for 𝜋 , find the area of this shape.

Q13:

Using 3.14 to approximate 𝜋 , what is the area of the shaded region?

Q14:

Calculate the area of the shaded region, using 3.14 in place of 𝜋 .

Q15:

Find the area of the given figure to the nearest tenth.

Q16:

Calculate the area of the shaded region. (If necessary, use as an approximation of .)

Q17:

Determine, to the nearest tenth, the area of the shaded region.

Q18:

In rhombus 𝐴 𝐵 𝐶 𝐷 , suppose that 𝐴 𝐶 + 𝐵 𝐷 = 2 6 0 , the ratio 𝐵 𝐷 𝐴 𝐶 : is 2 3 , and 𝑀 𝐸 = 1 2 𝑀 𝐴 . What is the area of the shaded region?

Q19:

Adel wants to paint one of the walls in his house; it is a rectangular wall with dimensions as seen in the given figure. He does not need to paint the door and will buy a gallon tin of paint that covers 400 square feet of wall. Work out what fraction of the tin will remain after he has painted the wall.

  • A
  • B
  • C221
  • D
  • E

Q20:

Yasmine wants to paint the frame of her arch window with dimensions as seen in the given figure. Find the area of that frame so that she would know how much paint is needed. Use rectangles and semicircles to model this shape.