Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.

2.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

3.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

4.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.

5.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.

6.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

7.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.

8.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

9.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

10.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?

11.A vertical line passes through the point (5, 2). Write down the equation of this line.

12.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

13.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

14.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.

15.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.