Geometry and measures worksheet — GCSE Foundation

1.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

2.A submarine travels due south. What is the three-figure bearing for this direction?

3.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

4.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

5.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

6.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

7.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

8.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².

9.Write down how many right angles a rectangle has.

10.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

11.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?

12.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.

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

14.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

15.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.