Worksheet: Areas of Composite Figures

In this worksheet, we will practice finding the area of a composite figure consisting of two or more shapes including polygons, circles, half circles, and quarter circles.

Q1:

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

Q2:

Using 3.14 as an estimate for πœ‹, calculate the area of the given figure.

Q3:

Find the area of the shaded part using 3.14 as an approximation for πœ‹.

Q4:

Chloe is interested in finding the area of circles. She has studied circumference and is happy with the formula 𝑐=2πœ‹π‘Ÿ, but she has not yet looked at area.

She starts off by drawing a circle with a square drawn on the inside and another on the outside. She uses these two squares to find an initial range that the area of the circle must lie between. What range does she get?

  • ABetween 16 and 24
  • BBetween 16 and 36
  • CBetween 30 and 36
  • DBetween 20 and 24
  • EBetween 30 and 32

By combining sections to make full squares, she decides she can comfortably improve her estimated range. She counts a further 8 squares inside the circle and a further 4 outside the circle. What is her improved range for the area?

  • ABetween 16 and 20
  • BBetween 32 and 36
  • CBetween 30 and 32
  • DBetween 24 and 32
  • EBetween 20 and 24

Chloe decides to take a more thorough approach to work out the area of her circle. She cuts it up into eight identical sectors and places them together to make a β€œparallelogram,” as seen in the given picture. She knows that the height of the parallelogram must be close to one radius, 3, and that the base of the parallelogram must be approximately half the circumference of the circle, which she knows is 2πœ‹π‘Ÿ2. To the nearest hundredth, what is the area of the circle?

Chloe wants to come up with the general formula for a circle. She realizes that if she divides her circle into more sectors and combines them, the shape gets closer to a parallelogram. If she split up her circle into infintely many sectors, the shape would tend to a perfect parallelogram. She knows the height of her parallelogram would become the radius of the circle, so she calls it π‘Ÿ. She also knows that the base is half the circumference, 2πœ‹π‘Ÿ2. Work out the area of the parallelogram to find a formula for the area of a circle.

  • A 𝐴 = πœ‹ π‘Ÿ + 2
  • B 𝐴 = ( πœ‹ + 1 ) π‘Ÿ
  • C 𝐴 = πœ‹ π‘Ÿ
  • D 𝐴 = πœ‹ π‘Ÿ 
  • E 𝐴 = 2 πœ‹ π‘Ÿ 

Q5:

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

Q6:

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

Q7:

𝐴 𝐡 𝐢 is an isosceles triangle, where 𝐴𝐡=𝐴𝐢=29cm and 𝐡𝐢=46cm. A circle with center 𝐴 touches 𝐡𝐢 at the point 𝐷, cutting 𝐴𝐡 at the point 𝐸 and cutting 𝐴𝐢 at the point 𝐹. Find the area of the part of the triangle bounded by 𝐸𝐡, 𝐡𝐢, 𝐢𝐹, and the arc 𝐹𝐸, giving the answer to two decimal places.

Q8:

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

Q9:

In this figure, the centers of three small, congruent circles are marked, and they lie on the diameter of a larger circle.

Find, to the nearest tenth, the area of the colored part.

Q10:

Using 3.14 as an approximation value for πœ‹, determine the area of the shaded part of this figure.

Q11:

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

Q12:

Find the area of the shape below using 227 as an approximation for πœ‹. Round your answer to two decimal places.

Q13:

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

Q14:

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

Q15:

Use 3.14 as an approximation of πœ‹ to find the area of this shape.

Q16:

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

Q17:

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.

Q18:

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

Q19:

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

Q20:

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

Q21:

A rectangle which measures 9.6 cm by 7.2 cm is drawn inside a circle with center 𝑀 and radius 6 cm. Using 3.14 as an estimate for πœ‹, find the area of the shaded part.

Q22:

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

Q23:

Find the area of this shape. (You may use 227 to approximate πœ‹.)

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.

  • A106 square inches
  • B260 square inches
  • C540 square inches
  • D280 square inches
  • E183 square inches

Q25:

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

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