Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

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1.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.
(a)72 cm²
(b)18 cm²
(c)36 cm²
(d)26 cm²
2.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?
(a)Wrong - none of the sides or angles match
(b)Correct, but by ASA rather than SAS
(c)Correct - two sides and an angle match
(d)Wrong - the given angle is not the included angle
3.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.
(a)1600
(b)500
(c)8
(d)16
4.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.
(a)33
(b)11
(c)36
(d)35
5.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.
(a)4√3 m
(b)12 m
(c)6√3 m
(d)3 m
6.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.
(a)32
(b)28
(c)24
(d)20
7.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?
(a)A cuboid
(b)A cone
(c)A square-based pyramid
(d)A cylinder
8.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.
(a)40 cm²
(b)120 cm²
(c)24 cm²
(d)15 cm²
9.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
(a)(1, 7)
(b)(6, 4)
(c)(6, 2)
(d)(−2, 4)
10.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
11.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².
(a)120 m²
(b)12 m²
(c)4.6 m²
(d)1.2 m²
12.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142
13.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
14.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.
(a)(8, 2)
(b)(−1, 11)
(c)(−4, 8)
(d)(8, 8)
15.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
(a)106°
(b)16°
(c)74°
(d)148°

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