Geometry and measures worksheet — GCSE Foundation

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

2.Write down the exact value of tan 0°.

3.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

4.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.

5.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

6.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

7.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.

8.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.

9.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

10.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

11.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

12.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?

13.Write down the exact value of sin 0°.

14.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

15.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.