Geometry and measures worksheet — GCSE Foundation

1.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

2.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

3.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

4.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

5.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

6.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.

7.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

8.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

9.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.

10.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

11.Which of the following is the correct definition of a regular polygon?

12.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

13.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

14.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

15.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?