Geometry and measures worksheet — GCSE Higher

1.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

2.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

3.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

4.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.

5.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

6.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.

7.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.

8.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.

9.A triangular plot of land has sides AB = 13 m and AC = 10 m, with angle BAC = 72° between them. Work out the perimeter of the plot. Give your answer to 1 decimal place.

10.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

11.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

12.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

13.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

14.Work out the distance between the points (−3, 4) and (5, −2).

15.Work out the distance between the point (0, 0) and the point (5, 12).