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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.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.
(a)5 cm
(b)30 cm
(c)12 cm
(d)15 cm
2.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.
(a)A square's diagonals are equal in length
(b)A square has only one pair of parallel sides
(c)A square's diagonals do not cross at right angles
(d)A square's sides are not all equal in length
3.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.
(a)59°
(b)118°
(c)62°
(d)236°
4.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
5.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.
(a)6 cm
(b)21 cm
(c)12 cm
(d)7.5 cm
6.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.
(a)104°
(b)38°
(c)52°
(d)128°
7.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?
(a)A cylinder
(b)A pyramid
(c)A cone
(d)A prism
8.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.
(a)8
(b)80
(c)0.8
(d)125
9.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
(a)24 cm
(b)26 cm
(c)6 cm
(d)10 cm
10.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?
(a)Yes — two sides and one angle match
(b)No — the angle given is not the included angle
(c)No — SSS needs three equal sides, not two
(d)Yes — SAS allows any equal angle, not just the included one
11.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
(a)18 cm
(b)3√3 cm
(c)9√3/2 cm
(d)9√3 cm
12.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.
(a)110°
(b)70°
(c)140°
(d)20°
13.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.
(a)110°
(b)40°
(c)220°
(d)140°
14.A square has sides of length 7 cm. Work out its area.
(a)49 cm²
(b)21 cm²
(c)28 cm²
(d)14 cm²
15.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?
(a)9
(b)6
(c)8
(d)5

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