Geometry and measures worksheet — GCSE Foundation

1.A cube has all of its edges the same length. How many planes of symmetry does it have?

2.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

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

4.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.

5.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

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

7.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

8.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

9.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

10.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

11.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

12.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.

13.A polygon has 9 sides. What is the name of this polygon?

14.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

15.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.