Geometry and measures worksheet — GCSE Foundation

1.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

2.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?

3.Write down the exact value of cos 30°.

4.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

5.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.

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

7.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

8.How many vertices does a cylinder have?

9.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

10.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

11.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

12.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?

13.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

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

15.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?