Geometry and measures worksheet — GCSE Foundation

1.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

2.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

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

4.Write down how many right angles a rectangle has.

5.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.

6.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

7.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

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

9.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

10.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

11.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.

12.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

13.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

14.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?

15.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.