Geometry and measures worksheet — GCSE Foundation

1.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

2.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.

3.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

4.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

5.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

6.In this question, a curved surface counts as a face. How many faces does a cone have?

7.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.

8.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

9.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

10.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

11.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

12.Write down the term for the distance all the way around the edge of a circle.

13.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

14.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.

15.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.