Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher 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 Higher

Maths · GCSE Higher · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.
(a)2312 cm
(b)8 cm
(c)16 cm
(d)119 cm
2.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.
(a)180 cm³
(b)66 cm³
(c)15 cm³
(d)360 cm³
3.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.
(a)Parallel, since A and D have the same x-coordinate
(b)Parallel, since AB and DC are both horizontal lines
(c)Not parallel, since AB is horizontal and DC is vertical
(d)Not parallel, since AB and DC have different lengths
4.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.
(a)4 cm
(b)8 cm
(c)10 cm
(d)12 cm
5.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.
(a)1909 cm²
(b)5091 cm²
(c)318 cm²
(d)2546 cm²
6.Triangle J is mapped onto triangle K by a single transformation with centre O. Triangle K is half the size of triangle J and is inverted (turned through 180°). Which of these transformations maps J onto K?
(a)An enlargement, centre O, scale factor −2.
(b)An enlargement, centre O, scale factor −1/2.
(c)A rotation of 180° about O, with no change in size.
(d)An enlargement, centre O, scale factor 1/2.
7.A shape is translated by the vector $(3 - 8)$ , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector $(- 5 2)$ . Work out the coordinates of the image of that same vertex under this second translation.
(a)(7, 8)
(b)(11, 3)
(c)(3, 1)
(d)(11, −2)
8.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.
(a)10.50 cm
(b)8.70 cm
(c)0.71 cm
(d)8.75 cm
9.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.
(a)3 cm
(b)6 cm
(c)8 cm
(d)30 cm
10.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?
(a)ASA
(b)SAS
(c)RHS
(d)SSS
11.Which of the following is the correct definition of a regular polygon?
(a)All of its sides are equal in length
(b)It has at least one line of symmetry
(c)Equal sides and equal interior angles
(d)All of its interior angles are equal
12.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.
(a)The angles are not necessarily equal
(b)Similar triangles are never congruent
(c)The scale factor is 2, not 1, so the sides are not equal
(d)Congruent triangles must have a right angle
13.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.
(a)(6, 1)
(b)(1, 6)
(c)(1, 5)
(d)(9, 6)
14.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?
(a)4.4
(b)110
(c)11
(d)1.1
15.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.
(a)9 : 4
(b)4 : 9
(c)2 : 3
(d)8 : 27

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