Geometry and measures worksheet — GCSE Foundation

1.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

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

3.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?

4.A footpath is 3750 m long. Work out this distance in kilometres.

5.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

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

7.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

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

9.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?

10.The perimeter of a square is 20 cm. Work out the area of the square.

11.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

12.What does the statement AB = CD mean, where A, B, C and D are all points?

13.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

14.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

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