Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Finding the Area of Composite Figures: Polygons and Sectors

Q1:

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

Q2:

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

Q3:

Noah 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 1 7 9 4 0 0
  • B 1 2
  • C221
  • D 2 2 1 4 0 0
  • E 3 7 9 4 0 0

Q4:

Determine, to the nearest tenth, the area of the given figure.

Q5:

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

Q6:

A quarter circle has been drawn inside a square such that the circle’s radius equals the square’s length. The area of the remaining part of the square is 47.18 cm2. Find, to the nearest centimeter, the side length of the square.

  • A 11 cm
  • B 8 cm
  • C 9 cm
  • D 15 cm

Q7:

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

Q8:

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

Q9:

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

Q10:

The diagram below shows a circle of radius π‘Ÿ cm inscribed in a triangle of base 7 𝑦 cm and height 3 π‘₯ 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œ‹ π‘Ÿ 2 . What is the degree of your area expression?

  • A The expression = 2 1 2 𝑦 π‘₯ , and it is of the second degree.
  • B The expression = 2 1 𝑦 π‘₯ βˆ’ πœ‹ π‘Ÿ 2 , and it is of the first degree.
  • C The expression = 2 1 𝑦 π‘₯ , and it is of the first degree.
  • D The expression = 2 1 2 𝑦 π‘₯ βˆ’ πœ‹ π‘Ÿ 2 , and it is of the second degree.

Q11:

Natalie 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.

  • A 280 square inches
  • B 540 square inches
  • C 106 square inches
  • D 183 square inches
  • E 260 square inches

Q12:

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

Q13:

In rhombus 𝐴 𝐡 𝐢 𝐷 , suppose that 𝐴 𝐢 + 𝐡 𝐷 = 1 0 8 , the ratio 𝐡 𝐷 𝐴 𝐢 : is 1 ∢ 2 , and 𝑀 𝐸 = 1 3 𝑀 𝐴 . What is the area of the shaded region?

Q14:

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

Q15:

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

Q16:

In rectangle 𝐴 𝐡 𝐢 𝐷 , a circle is removed that touches both sides 𝐴 𝐡 and 𝐷 𝐢 . Using 3.14 to approximate πœ‹ , what is the area of the remaining piece?

Q17:

Olivia has sketched a rough design for her rectangular garden as seen in the given figure. She has found that one pound of grass seed will cover about 300 square feet.

What is the area of grass in her garden? Give your answer in square feet to two decimal places.

  • A 391.73 square feet
  • B 568.87 square feet
  • C 439.16 square feet
  • D 553.16 square feet
  • E 379.16 square feet

How many pounds of grass seed will she need to buy? Give your answer accurate to two decimal places.

  • A 1.84 pounds
  • B 1.28 pounds
  • C 1.85 pounds
  • D 1.48 pounds
  • E 1.38 pounds

Q18:

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

Q19:

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

Q20:

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