An arc is part of a curve. When describing an arc of a circle, it is part of the circle's circumference.

Perimeter of composite shapes

Maths

Checking understanding of perimeter

Checking understanding of area

Multiplicative relationships in circles

Circumference of a circle

Area of a circle

Using the formula for the area of a circle

Area of composite shapes

Finding a length in composite shapes

Surface area of cuboids

Properties of prisms

Surface area of prisms

Surface area of cylinders

Volume of prisms

Volume of cylinders

Problem solving with perimeter, area and volume

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.

In this unit pupils extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.

Perimeter, area and volume

A quarter-circular sector is cut out of a circle. The original circle had a perimeter of 60$$\pi$$ cm. What is the arc length of this sector?

A semicircular sector is cut out of a circle. The radius of the original circle is 31 cm, and its circumference is 194.8 cm (rounded to 1 decimal place). What is the perimeter of the sector?

Calculate the perimeter of this sector, giving your answer in cm and rounding your answer to 1 decimal place.

This composite shape is composed of a circular sector and a square. Which of these statements are true about the perimeter of this composite shape that has been broken into component lengths.

This composite shape is composed of two quarter-circles and a rectangle. Match the statement about the component parts of the composite shape's perimeter to the correct value.

The square at the centre of this composite shape has an area of 441 cm². Find the perimeter of the composite shape in cm, rounded to the nearest integer.

What is $${1\over4}$$ of 76$$\pi$$ cm? Give your answer in decimal form and rounded to 2 decimal places. {{ }}

Which of these units of measurement is appropriate for measuring the perimeter of something?

$$circumference = 2{\times} {\pi} {\times}r$$

$$circumference = 2{\times}{\pi} {\times}d$$

Which of these formulae finds the circumference of a circle with radius $$r$$ and diameter $$d$$?

Which of these describes the circumference of a circle with a diameter of 60 cm?

A circular hoop with a radius of 40 cm is cut into 12 equally-sized pieces. What is the length of one piece? Give your answer in cm, rounded to 1 decimal place. {{ }} cm

Circle A has a radius of 49 cm. Circle B has a diameter of 1.33 metres. How much longer is the circumference of circle B than circle A? Give your answer in cm, rounded to the nearest integer.

Perimeter of composite shapes

Lesson outcome