Geometry and measures worksheet — GCSE Higher

1.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.

2.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.

3.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

4.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

5.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

6.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?

7.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

8.Work out the distance between the points (−3, 4) and (5, −2).

9.Triangle E has vertices (1, 2), (4, 2) and (1, 5). It is rotated 90° anticlockwise about the origin, and the image is then reflected in the line y = x. Work out the coordinates of the image of (4, 2).

10.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

11.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

12.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

13.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

14.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

15.A shape is reflected in the x-axis and the image is then reflected in the y-axis. Which single transformation is equivalent to this combination for every point?