Printable · GCSE Foundation · ages 14-16
Geometry and measures worksheet — GCSE Foundation
Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Geometry and measures worksheet — GCSE Foundation
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- 1.A regular nonagon has 9 sides. Work out the sum of its interior angles.
- 2.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.
- 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 map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?
- 5.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?
- 6.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?
- 7.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?
- 8.Work out the exact value of (sin 30°)² + (cos 30°)².
- 9.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
- 10.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.
- 11.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 12.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.
- 13.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.
- 14.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.
- 15.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.
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