Geometry and measures worksheet — GCSE Foundation

1.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

2.Work out the exact value of sin 45° × cos 45°.

3.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

4.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.

5.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?

6.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

7.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.

8.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

9.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

10.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

11.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

12.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

13.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

14.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

15.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)