Geometry and measures worksheet — GCSE Foundation

1.A polygon has 9 sides. What is the name of this polygon?

2.The perimeter of a square is 20 cm. Work out the area of the square.

3.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

4.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?

5.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

6.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

7.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.

8.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

9.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

10.Which of the following is the correct definition of a regular polygon?

11.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

12.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

13.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

14.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

15.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.