Geometry and measures worksheet — GCSE Foundation

1.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

2.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

3.An angle measures 108°. Write down the name given to an angle of this size.

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

5.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

6.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

7.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

8.A circle has a diameter of 4 cm. Work out the radius of the circle.

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

10.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

11.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?

12.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

13.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.

14.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.

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