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

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

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

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

Area of a sector

Maths

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.

2D and 3D shape: compound shapes

The sector comes from this circle. The area of the sector is {{ }} cm².

The area of a circle is 294 cm². The circle is split into 7 congruent sectors. The area of each sector is {{ }} cm².

Use the ratio table to identify which of these expressions and values are correct for the area of this sector.

The area is $${80\over360}\times30^2\pi$$ cm². 

Which of these statements are correct about this shape?

The area of this sector is {{ }} cm² (correct to 2 d.p.)

The area of sector A is 20 cm². Sector B is similar to sector A. The area of sector B is {{ }} cm².

The diameter of a circle is 30 cm. Which of the following statements about this circle are correct?

The perimeter of this shape is 108 cm. The value of $$y$$ is {{ }}.

Which of these statements are correct for this trapezium?

The perimeter of this shape is 48 cm. Which of these equations can be used to find the value of $$x$$?

The perimeter of this trapezium is 48 cm. The area of the trapezium is {{ }}cm².

The arc length of this sector is {{ }} cm (correct to 1 d.p.)

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