Geometry and measures worksheet — GCSE Foundation

1.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

2.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.

3.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

4.How many edges does a triangular prism have?

5.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

6.Write down the exact value of cos 45°.

7.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

8.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

9.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?

10.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

11.Write down the exact value of cos 30°.

12.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

13.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

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

15.Work out the exact value of (cos 45°)² + (sin 45°)².