Geometry and measures worksheet — GCSE Foundation

1.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.

2.Write down the name given to a triangle whose three sides are all the same length.

3.Write down the exact value of tan 60°.

4.A vertical line passes through the point (5, 2). Write down the equation of this line.

5.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

6.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

7.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

8.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.

9.In geometry, which of the following best describes a 'plane'?

10.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)

11.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

12.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

13.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

14.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

15.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?