An arc is part of a curve. An arc of a circle is part of the circle’s circumference.

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

A chord is any line segment joining two points on the circumference of a circle.

The radius is any line segment that joins the centre of a circle to any point on its circumference.

The circumference of a circle is the perimeter of the circle.

Calculating arc length

Maths

Checking and securing understanding of converting between metric and imperial measures

Checking and securing understanding of scales and conversion

Checking and securing understanding of perimeter for standard shapes

Checking and securing understanding of perimeter for compound shapes

Checking and securing understanding of area for standard shapes

Checking and securing understanding of area for compound shapes

Perimeter and area in a contextual setting

Checking and securing understanding of circles

Area of a sector

Area of compound shapes

Problem solving with 2D shapes

In this unit, pupils built upon their prior learning of the area of different shapes. In the future unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

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

In this unit, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.

2D and 3D shape: compound shapes

The sector comes from this circle. 
The arc length of this sector is {{ }} cm.

The sector comes from this circle.
The perimeter of the sector is {{ }} cm.

The arc length of the semicircle is 5 cm.

The arc length of the semicircle is 10$$\pi$$ cm.

The arc length of the semicircle is 20$$\pi$$ cm.

The perimeter of the semicircle is (10$$\pi$$ + 10) cm.

The perimeter of the semicircle is (10$$\pi$$ + 20) cm.

The radius of a circle is 10 cm. 
The circumference of the circle is 20$$\pi$$ cm. 

A semicircle is taken from this circle. 
Which of these statements are correct about this semicircle?

The arc length is $${80\over360}\times30\pi$$.

The arc length is $${80\over360}\times60\pi$$.

The arc length is $${40\over3}\times\pi$$.

The arc length is 42 cm (nearest integer).

Which of these statements are correct about the arc length of this sector?

The perimeter of this sector is {{ }} cm (to the nearest centimetre).

The diagram shows a sector. The chord between the endpoints of its radii is 350 cm.
The arc length of the sector is {{ }} cm (to the nearest centimetre).

The circumference is 119 cm (nearest integer).

The circumference is 238 cm (nearest integer).

A circle has a diameter of 38 cm.
Which of these are correct for the circumference of this circle?

A circle has a radius of 600 cm.
Which of these are correct for the area of this circle?

The perimeter of shape B is {{ }} cm bigger than the perimeter of shape A.

The perimeter of this shape is {{ }} metres.

Use Pythagoras’ theorem to help you complete this statement. The perimeter of the triangle is {{ }} cm correct to 1 d.p.

Calculating arc length

Lesson outcome