Area of composite shapes | Maths | Quizalize & Oak National Academy

Starter quiz

What is ${2\over3}$ of 144 cm?
- 96
- 96 cm ✓
- 216
- 216 cm
Which of these formulae finds the area of a circle with radius $r$ ?
- $area = {\pi} {\times}r$
- $area = 2{\times}{\pi} {\times}r$
- $area = {\pi} {\times}r2$
- $area = {\pi} {\times}r^2$ ✓
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
- 625 $\pi$ cm² ✓
- 1963.4 cm²
- 1963.5 cm² ✓
From its centre, this circle has been split up into 9 equally-sized sectors. How many degrees is the angle marked x?______
- '40' ✓
Match each statement to the correct value for a circle with a diameter of 80 units.
- The radius is
  
  ⇔
  
  40 ✓
- The area in terms of $\pi$
  
  ⇔
  
  1600 $\pi$ ✓
- The area in decimal form is
  
  ⇔
  
  5026.5 ✓
- The circumference is
  
  ⇔
  
  80 $\pi$ ✓
Which of these statements is true for this composite shape?
- $a$ = 7 cm
- $a$ = 15 cm ✓
- $a$ = 18 cm
- The area of the composite shape is 1128 cm². ✓
- The area of the composite shape is 1190 cm².

Exit quiz

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?
- 30 $\pi$ cm² ✓
- 40 $\pi$ cm²
- 94.25 $\pi$ cm²
- 480 $\pi$ cm²
- 94.25 cm² ✓
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.
- '512' ✓
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.
- 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.
- The area of this sector is 363 $\pi$ cm². ✓
- The area of this sector is 484 $\pi$ cm².
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.
- area of square
  
  ⇔
  
  4 cm² ✓
- area of semicircle
  
  ⇔
  
  ${1\over2}\pi$ cm² ✓
- area of quarter-circle
  
  ⇔
  
  3.14 cm² ✓
- area of composite shape
  
  ⇔
  
  8.71 cm² ✓
$Which of these shows the area (written in terms of <Math>\pi</Math>) of the shaded region of this composite shape composed of a circular sector and a square?$

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
- (2304 − 288 $\pi$ ) cm² ✓
What is the area (in cm²) of this composite shape, composed of only squares and circular sectors, rounded to the nearest integer? ______cm²
- '393' ✓

Worksheet

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Presentation

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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.

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.

Keywords

Sector - A sector is the region formed between two radii and their connecting arc.