Geometry and measures worksheet — GCSE Foundation

1.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

2.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

3.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.

4.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.

5.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.

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

7.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

8.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

9.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

10.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

11.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.

12.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

13.An angle is measured with a protractor as 47°. What type of angle is this?

14.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

15.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².