Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC has a right angle at B, hypotenuse AC = 13 cm and AB = 5 cm. Triangle DEF has a right angle at E, hypotenuse DF = 13 cm and DE = 5 cm. Which condition proves the two triangles are congruent?

2.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

3.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

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

5.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?

6.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.

7.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

8.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

9.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

10.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

11.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

12.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.

13.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

14.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

15.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².