Geometry and measures worksheet — GCSE Foundation

1.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

2.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

3.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

4.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

5.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

6.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

7.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

8.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

9.Each of these has an exact value. Write down the one whose value is the greatest.

10.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

11.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

12.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

13.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

14.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.

15.Write down the name given to a triangle whose three sides are all the same length.