Geometry and measures worksheet — GCSE Foundation

1.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

2.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

3.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

4.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.

5.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?

6.Which of the following correctly describes what it means for two lines to be perpendicular?

7.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

8.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

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.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

11.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

12.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

13.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

14.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

15.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.