Geometry and measures worksheet — GCSE Foundation

1.A water tank holds 2.5 m³. Work out this volume in cm³.

2.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.

3.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

4.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

5.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

6.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

7.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

8.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

9.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

10.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

11.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

12.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

13.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.

14.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

15.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.