Problem solving with complex 2D shapes | Maths | Quizalize & Oak National Academy

Starter quiz

A ______ is a circular graph where sectors represent different groups proportionally.

'pie chart' ✓
Jacob wants to plot a pie chart to represent the data in the table. What angle for the sector representing 'museum' should Jacob use?

8°

18°

20°

45°

144° ✓
A circle has diameter 10 cm. Its area is ____ $\pi$ cm².

'25' ✓
The diagram shows a sector of a circle with radius 10 cm. The angle at the centre of the sector is 70°. Which calculation would find the area of the sector?

$\frac{70}{360} \times \pi \times 10$

$\frac{70}{360} \times 2 \times \pi \times 10$

$\frac{70}{360} \times \pi \times 5^2$

$\frac{70}{360} \times \pi \times 10^2$ ✓

$\frac{70}{360} \times \pi \times 20^2$
$The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The area of the sector is <span class="blank">______</span><Math>\pi</Math> cm².$

The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The area of the sector is ______ $\pi$ cm².

'24' ✓
The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The perimeter of the sector is ______ cm (to one decimal place).

'36.5' ✓

Exit quiz

The diagram shows a square inscribed inside a circle. The length of the square is 6 cm. What is the diameter of the circle?

$3$ cm

$6$ cm

$3\sqrt{2}$ cm

$6\sqrt{2}$ cm ✓

$12\sqrt{2}$ cm
The diagram shows a square inscribed inside a circle. The diameter of the circle is 6 cm. Work out the length of the square.

$3$ cm

$6$ cm

$3\sqrt{2}$ cm ✓

$6\sqrt{2}$ cm

$12\sqrt{2}$ cm
$The diagram shows a square inscribed inside a circle. The length of the square is 8 cm. The area of the circle is <span class="blank">______</span><Math>\pi</Math> cm².$

The diagram shows a square inscribed inside a circle. The length of the square is 8 cm. The area of the circle is ______ $\pi$ cm².

'32' ✓
The diagram shows a square inscribed inside a circle. The diameter of the circle is 8 cm. The area of the square is ______cm².

'32' ✓
The diagram shows a square inscribed inside a circle. The diameter of the circle is 12 cm. Which calculation would find the area of the shaded region?

$\pi \times 6^2 - (3\sqrt{2})^2$

$\pi \times 6^2 - (6\sqrt{2})^2$ ✓

$\pi \times 12^2 - (3\sqrt{2})^2$

$\pi \times 12^2 - (6\sqrt{2})^2$
The diagram shows a square inscribed inside a circle. The length of the square is 12 cm. The area of the shaded region is ______ cm² (to one decimal place).

'82.2' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

When problem solving, consider whether any elements are familiar from other areas of maths.
Keep the goal in mind, it is easy to get distracted by too much information.
The size of a sector of a pie chart can be scaled to reflect the population size.

Common misconception

For the problems with squares inscribed inside circles, pupils may think that the length of the square is equal to the diameter of the circle.

This would be the case if the circle was inscribed inside a square. But when the square is inscribed inside a circle, the diagonal length of the square is equal to the diameter of the circle.

Keywords

Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Compound shape - A compound shape is a shape created using two or more basic shapes.
Composite shape - A composite shape is an alternative for a compound shape.
Pie chart - A pie chart (pie graph) is a circular graph where sectors represent different groups proportionally.