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

Q1:

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

Q2:

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

Q3:

The diagram below shows a circle of radius cm inscribed in a triangle of base cm and height cm. Find an expression for the area, in cm2, of the shaded region given that the area of a circle is given by . What is the degree of your area expression?

  • AThe expression , and it is of the first degree.
  • BThe expression , and it is of the second degree.
  • CThe expression , and it is of the second degree.
  • DThe expression , and it is of the first degree.

Q4:

Using the approximation for , calculate the area of the shaded part.

Q5:

Find the area of the shaded region, using to approximate .

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

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

Q14:

If a new carpet is needed for the theater shown in the figure, determine the area of the carpet rounded to the nearest square yard.

Q15:

The figure shows the dimensions of a putting green at a miniature golf course. Determine, to 2 decimal places, how many square feet of carpet are needed to cover the green.

Q16:

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

Q17:

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

Q18:

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

Q19:

The shown figure represents a circle inside a regular hexagon. Find the area of the shaded regions, giving your answer to the nearest tenth.

Q20:

Find the area of the shaded region rounded to the nearest tenth.

Q21:

In rhombus , suppose that , the ratio is , and . What is the area of the shaded region?

Q22:

Find the total area of the shaded regions in the regular polygons below, giving your answer to the nearest tenth.

Q23:

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
  • B221
  • C
  • D
  • E

Q24:

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.