Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

2.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

3.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

4.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

5.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

6.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

7.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

8.Work out the exact value of (cos 45°)² + (sin 45°)².

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

10.A regular nonagon has 9 sides. Work out the sum of its interior angles.

11.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

12.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

13.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

14.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

15.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.