New
New
Area of composite shapes
I can solve area problems of composite shapes involving whole and/or part circles.
Lesson 7 of 16
New
New
- Year 8
Area of composite shapes
I can solve area problems of composite shapes involving whole and/or part circles.
Lesson details
Key learning points
- The area parts of a circle can be found using the area formula and reasoning.
- The area of shapes made from circles and parts of circles can be found.
- The area of composite shapes that include circles can be found.
Keywords
Sector - A sector is the region formed between two radii and their connecting arc.
Common misconception
To find the area of a quarter-circle divide the radius by 4 to use as part of the calculation.
You must divide the area by 4, not the radius. The radius gets squared when calculating area so the division of r would be applied twice.
Encourage students to sketch the component parts of each composite shape. This is especially helpful in visualising the shape of both the negative and positive space in a composite shape with a component part removed from the object.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is $${2\over3}$$ of 144 cm?
What is $${2\over3}$$ of 144 cm?
96
Correct answer: 96 cm
96 cm
216
216 cm
Q2.Which of these formulae finds the area of a circle with radius $$r$$?
Which of these formulae finds the area of a circle with radius $$r$$?
$$area = {\pi} {\times}r$$
$$area = 2{\times}{\pi} {\times}r$$
$$area = {\pi} {\times}r2$$
Correct answer: $$area = {\pi} {\times}r^2$$
$$area = {\pi} {\times}r^2$$
Q3.Find the area of a circle with radius of 25 cm, giving your answer both in terms of $$\pi$$ and in decimal form, rounded to 1 decimal place.
Find the area of a circle with radius of 25 cm, giving your answer both in terms of $$\pi$$ and in decimal form, rounded to 1 decimal place.
25$$\pi$$ cm²
50$$\pi$$ cm²
Correct answer: 625$$\pi$$ cm²
625$$\pi$$ cm²
1963.4 cm²
Correct answer: 1963.5 cm²
1963.5 cm²
Q4.From its centre, this circle has been split up into 9 equally-sized sectors. How many degrees is the angle marked x?
From its centre, this circle has been split up into 9 equally-sized sectors. How many degrees is the angle marked x?
Correct Answer: 40, 40°, 40degrees, 40 degrees
40, 40°, 40degrees, 40 degrees
Q5.Match each statement to the correct value for a circle with a diameter of 80 units.
Match each statement to the correct value for a circle with a diameter of 80 units.
Correct Answer:The radius is,40
The radius is - 40
Correct Answer:The area in terms of $$\pi$$,1600$$\pi$$
The area in terms of $$\pi$$ - 1600$$\pi$$
Correct Answer:The area in decimal form is,5026.5
The area in decimal form is - 5026.5
Correct Answer:The circumference is,80$$\pi$$
The circumference is - 80$$\pi$$
Q6.Which of these statements is true for this composite shape?
Which of these statements is true for this composite shape?
$$a$$ = 7 cm
Correct answer: $$a$$ = 15 cm
$$a$$ = 15 cm
$$a$$ = 18 cm
Correct answer: The area of the composite shape is 1128 cm².
The area of the composite shape is 1128 cm².
The area of the composite shape is 1190 cm².
Assessment exit quiz
6 Questions
Q1.A quarter-circular sector is cut out of a circle. The original circle had an area of 120$$\pi$$ cm². What is the area of the quarter-circle?
A quarter-circular sector is cut out of a circle. The original circle had an area of 120$$\pi$$ cm². What is the area of the quarter-circle?
Correct answer: 30$$\pi$$ cm²
30$$\pi$$ cm²
40$$\pi$$ cm²
94.25$$\pi$$ cm²
480$$\pi$$ cm²
Correct answer: 94.25 cm²
94.25 cm²
Q2.A sector with a 60° angle is cut out of a circle. The original circle had an area of 3072 inches². The area of the sector is square inches.
A sector with a 60° angle is cut out of a circle. The original circle had an area of 3072 inches². The area of the sector is square inches.
Correct Answer: 512, 512 square inches, 512 inches²
512, 512 square inches, 512 inches²
Q3.Which of the following statements is true for this sector?
Which of the following statements is true for this sector?
This sector is $$2\over3$$ the area of a circle that has the same radius.
Correct answer: This sector is $$3\over4$$ the area of a circle that has the same radius.
This sector is $$3\over4$$ the area of a circle that has the same radius.
The area of this sector is 16.5$$\pi$$ cm².
Correct answer: The area of this sector is 363$$\pi$$ cm².
The area of this sector is 363$$\pi$$ cm².
The area of this sector is 484$$\pi$$ cm².
Q4.This composite shape is broken down into its component parts, made from circular sectors and quadrilaterals. Match each component part and composite shape to its area.
This composite shape is broken down into its component parts, made from circular sectors and quadrilaterals. Match each component part and composite shape to its area.
Correct Answer:area of square,4 cm²
area of square - 4 cm²
Correct Answer:area of semicircle,$${1\over2}\pi$$ cm²
area of semicircle - $${1\over2}\pi$$ cm²
Correct Answer:area of quarter-circle,3.14 cm²
area of quarter-circle - 3.14 cm²
Correct Answer:area of composite shape,8.71 cm²
area of composite shape - 8.71 cm²
Q5.Which of these shows the area (written in terms of $$\pi$$) of the shaded region of this composite shape composed of a circular sector and a square?
Which of these shows the area (written in terms of $$\pi$$) of the shaded region of this composite shape composed of a circular sector and a square?
2304 cm²
(2304 + 576$$\pi$$) cm²
(2304 + 288$$\pi$$) cm²
(2304 − 576$$\pi$$) cm²
Correct answer: (2304 − 288$$\pi$$) cm²
(2304 − 288$$\pi$$) cm²
Q6.What is the area (in cm²) of this composite shape, composed of only squares and circular sectors, rounded to the nearest integer? cm²
What is the area (in cm²) of this composite shape, composed of only squares and circular sectors, rounded to the nearest integer? cm²
Correct Answer: 393, 393 cm², 393cm²
393, 393 cm², 393cm²
