Geometry and measures worksheet — GCSE Higher

1.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.

2.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

3.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.

4.Which of these statements about the area formula Area = 1/2ab sin C is correct?

6.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

7.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

8.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.

9.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?

10.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

11.A rotation of 180° about the point (3, 2) can be written as a reflection in the line x = 3, followed by a reflection in a second line, for every point in the plane. Which line is the second line?

12.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

13.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

14.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

15.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?