Geometry and measures worksheet — GCSE Foundation

1.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

2.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

3.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

4.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

5.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

6.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

7.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

8.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

9.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

10.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

11.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

12.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

13.Write down the exact value of cos 45°.

14.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

15.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.