Geometry and measures worksheet — GCSE Higher

1.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.

2.In triangle ABC, AB = 8 cm, AC = 5 cm and angle BAC = 60°. Work out the value of BC².

3.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

4.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.

5.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

6.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

7.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

8.A, B and C are points on a circle with centre O, and AC is a diameter of the circle. Work out the size of angle ABC.

9.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

10.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².

11.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

12.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

13.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

14.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

15.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?