Geometry and measures worksheet — GCSE Foundation

1.A square has sides of length 7 cm. Work out its area.

2.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

3.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

4.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

5.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

6.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

7.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

8.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?

9.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

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

11.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

12.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

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

14.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

15.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.