Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?

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

3.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

4.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

5.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

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

7.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

8.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

9.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

10.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.

11.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

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

13.A flower bed in the shape of a parallelogram has a base of 3.5 m and a perpendicular height of 2 m. Compost costs £4.80 per m². Work out the total cost of covering the flower bed with compost.

15.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.