Geometry and measures worksheet — GCSE Foundation

1.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.

2.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

3.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

4.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

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

6.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

7.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

8.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

9.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

10.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

11.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

13.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

14.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

15.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.