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

Start Practicing

Worksheet: Area of a Composite Figure

Q1:

What is the area of this shape?

Q2:

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

Q3:

The circle at 𝑂 has radius 34 cm. Chord 𝐴 𝐡 is 60 cm long, 𝐢 is the midpoint of 𝐴 𝐡 , and ray  𝑂 𝐢 meets the circle at 𝐷 . Find the area of β–³ 𝐴 𝐷 𝐡 .

  • A 1,020 cm2
  • B 1,080 cm2
  • C 128 cm2
  • D 540 cm2

Q4:

𝐴 𝐡 𝐢 is an isosceles triangle inscribed in a circle where 𝐴 𝐡 = 𝐴 𝐢 = 3 7 cm and 𝐡 𝐢 = 3 8 c m . Find the area of the minor segment with chord 𝐡 𝐢 giving the answer to the nearest square centimeter.

  • A 615 cm2
  • B 154 cm2
  • C 695 cm2
  • D 308 cm2

Q5:

Triangle 𝐴 𝐡 𝐢 is right-angled at 𝐡 . Given that π‘š ∠ 𝐴 = 3 0 ∘ , and 𝐴 𝐡 = 6 8 . 2 . Find to the nearest hundredth the area of the circle that lies on 𝐴 and 𝐡 and is tangent to 𝐴 𝐢 at 𝐴 .

Q6:

Two circles intersect each other where the chord connecting the points of intersection is a diameter of one of the circles. The length of the diameter is 76 cm which is the same length of the radius of the other circle. Find the common area between the two circles giving the answer to two decimal places.

Q7:

Determine the area of the shown figure.

Q8:

The picture shows the design of a logo which is formed from two semicircles with a common center.

Work out the perimeter of the logo, giving your answer in terms of πœ‹ .

  • A 1 6 πœ‹ + 8
  • B 8 πœ‹ βˆ’ 1 6
  • C 1 6 πœ‹ βˆ’ 8
  • D 8 πœ‹ + 4
  • E 1 6 πœ‹

Work out the area of the logo, giving your answer in terms of πœ‹ .

  • A 1 7 πœ‹
  • B 1 0 πœ‹
  • C 1 1 πœ‹
  • D 1 3 πœ‹
  • E 7 πœ‹

Q9:

Chloe is interested in finding the area of circles. She has studied circumference and is happy with the formula 𝑐 = 2 π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 30 and 32
  • BBetween 30 and 36
  • CBetween 16 and 24
  • DBetween 16 and 36
  • EBetween 20 and 24

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 24 and 32
  • BBetween 16 and 20
  • CBetween 30 and 32
  • DBetween 32 and 36
  • 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 2 πœ‹ π‘Ÿ 2 . 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, 2 πœ‹ π‘Ÿ 2 . 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 = 2 πœ‹ π‘Ÿ 2
  • C 𝐴 = πœ‹ π‘Ÿ + 2
  • D 𝐴 = πœ‹ π‘Ÿ
  • E 𝐴 = ( πœ‹ + 1 ) π‘Ÿ

Q10:

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

Q11:

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

Q12:

Given that 𝐴 𝐡 𝐢 𝐷 is a rectangle in which 𝐴 𝐷 = 2 0 c m , find its area.

Q13:

Determine the area of the given figure.

Q14:

Find the area of this shape.

Q15:

Find the area of the given figure.

Q16:

Determine the area of the given figure.

Q17:

Determine the area of the given figure.

Q18:

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

Q19:

Calculate the area of the given figure.

Q20:

Given that the four triangles in the shown rectangle are congruent, calculate the area of the colored region.

Q21:

Determine the area of the given figure.

Q22:

Determine the area of the given figure.

Q23:

Find the area of this figure.

Q24:

Find the area of the given figure.