Geometry and measures worksheet — GCSE Foundation

1.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

2.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

3.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

4.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

5.What does the statement AB = CD mean, where A, B, C and D are all points?

6.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

7.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.

8.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

9.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

10.A polygon has 12 straight sides. What is the mathematical name for this polygon?

11.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

12.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?

13.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

14.Write down the column vector, from the options given, that would move a point to the right and downwards.

15.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.