Geometry and measures worksheet — GCSE Foundation

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

2.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

3.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

4.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.

5.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

6.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

7.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

8.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

9.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

10.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.

11.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

12.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

13.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

14.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

15.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.