Geometry and measures worksheet — GCSE Foundation

1.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

2.Work out the exact value of cos 0° − sin 30°.

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

4.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

5.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.

6.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

7.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

8.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

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

11.A water tank holds 2.5 m³. Work out this volume in cm³.

12.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

13.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

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

15.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?