Geometry and measures worksheet — GCSE Foundation

1.Write down the number of lines of symmetry a rhombus has.

2.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

3.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

4.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.

5.Work out the exact value of tan 30° + tan 30°.

6.A submarine travels due south. What is the three-figure bearing for this direction?

7.A polygon has one more side than a heptagon. What is the polygon called?

8.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

9.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

10.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

11.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

12.How many edges does a cube have?

13.A polygon has 12 straight sides. What is the mathematical name for this polygon?

14.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.

15.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?