Geometry and measures worksheet — GCSE Foundation

1.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

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

3.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

4.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

5.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

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

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

8.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.

9.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

10.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

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

12.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

13.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.

14.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

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