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.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.
(a)28 cm
(b)14 cm
(c)49 cm
(d)11 cm
2.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.
(a)228°
(b)48°
(c)66°
(d)132°
3.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
(a)64°
(b)32°
(c)58°
(d)122°
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 straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m
6.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.
(a)Isosceles trapezium: base angles are equal
(b)Rhombus: all four angles are equal
(c)Kite: one pair of opposite angles equal
(d)Parallelogram: opposite angles are equal
7.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.
(a)12 cm
(b)768 cm
(c)104 cm
(d)24 cm
8.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.
(a)59°
(b)118°
(c)62°
(d)31°
9.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?
(a)RHS - right angle, hypotenuse and one side equal
(b)SAS - two sides and the included angle equal
(c)AAS - two angles and a non-included side equal
(d)ASA - two angles and the included side equal
10.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
(a)A smaller circle
(b)A triangle
(c)The same size circle as the base
(d)An ellipse
11.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.
(a)68°
(b)170°
(c)78°
(d)184°
12.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
(a)22
(b)28
(c)35
(d)63
13.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
14.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
15.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
(a)angles round a point add up to 360°
(b)angles on a straight line add up to 180°
(c)vertically opposite angles are equal
(d)angles in a triangle add up to 180°

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