Geometry and measures worksheet — GCSE Foundation

1.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.

2.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

3.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

4.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.

5.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

6.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

7.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

8.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.

9.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

10.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

11.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

12.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

13.In this question, a curved surface counts as a face. How many faces does a sphere have?

14.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.

15.An angle measures 108°. Write down the name given to an angle of this size.