Geometry and measures worksheet — GCSE Foundation

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

2.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.

3.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

4.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

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

6.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

7.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

8.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

9.A hiker walks due west. What is the three-figure bearing for this direction?

10.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

11.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

12.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

13.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?

14.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

15.A square tile has sides of length 6 cm. Work out the area of the tile.