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

Area of composite shapes

Maths

In this unit, pupils have derived the formula for the circumference and area of a circle. In the future unit, this knowledge is combined with knowledge of fractions to find the arc length and area of a sector.

 In the prior unit, pupils learnt how to derive and use the formula for the area of a triangle and trapezium. In this unit, this knowledge is called upon to find the volume of different prisms and area of composite shapes.

Perimeter, area and volume

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 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.

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.

Which of the following statements is true for this sector?

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.

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?

What is the area (in cm²) of this composite shape, composed of only squares and circular sectors, rounded to the nearest integer? {{}}cm²

Which of these formulae finds the area of a circle with radius $$r$$?

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.

From its centre, this circle has been split up into 9 equally-sized sectors. How many degrees is the angle marked x?{{ }}

Match each statement to the correct value for a circle with a diameter of 80 units.

The area of the composite shape is 1128 cm².

The area of the composite shape is 1190 cm².

Which of these statements is true for this composite shape?

Area of composite shapes

Lesson outcome