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AQA GCSE Maths: Geometry and measures — Practice Questions & Answers
A complete tour of GCSE geometry: angle facts and polygons, triangle and quadrilateral properties, circle theorems, perimeter, area and sectors, surface area and volume of solids, Pythagoras in 2D and 3D, right-angled trigonometry with exact values, the sine and cosine rules and the area formula, bearings, congruence and similarity, transformations, vectors, and constructions and loci.
498 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
The angles on a straight line are $x$ and $130^{\circ}$. What is the value of $x$?
$50^{\circ}$
$230^{\circ}$
$130^{\circ}$
$70^{\circ}$
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Why Angles on a straight line add to $180^{\circ}$, so $x=180-130=50^{\circ}$.
2
Multiple choice · Easy
Three angles meet at a point. Two of them are $90^{\circ}$ and $150^{\circ}$. What is the third angle?
$120^{\circ}$
$60^{\circ}$
$240^{\circ}$
$30^{\circ}$
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Why Angles around a point add to $360^{\circ}$, so the third angle is $360-90-150=120^{\circ}$.
3
Multiple choice · Easy
A regular hexagon has $6$ sides. What is the size of each exterior angle?
$60^{\circ}$
$120^{\circ}$
$720^{\circ}$
$45^{\circ}$
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Why The exterior angles of any polygon sum to $360^{\circ}$, so each is $\frac{360}{6}=60^{\circ}$.
4
Multiple choice · Easy
Two parallel lines are crossed by a straight line. One of the co-interior (allied) angles is $70^{\circ}$. What is the other co-interior angle?
$110^{\circ}$
$70^{\circ}$
$290^{\circ}$
$20^{\circ}$
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Why Co-interior angles between parallel lines add to $180^{\circ}$, so the other angle is $180-70=110^{\circ}$.
5
Multiple choice · Easy
A rectangle has length $8$ cm and width $5$ cm. What is its perimeter?
$26$ cm
$40$ cm
$13$ cm
$80$ cm
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Why Perimeter $=2(8+5)=26$ cm. A common error is computing the area $8\times 5=40$ instead.
6
Multiple choice · Easy
A triangle has base $10$ cm and perpendicular height $6$ cm. What is its area?
$30$ cm$^{2}$
$60$ cm$^{2}$
$16$ cm$^{2}$
$32$ cm$^{2}$
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Why Area of a triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 10\times 6=30$ cm$^{2}$.
7
Multiple choice · Easy
An isosceles triangle has a vertex angle of $40^{\circ}$. What is the size of each base angle?
$70^{\circ}$
$140^{\circ}$
$40^{\circ}$
$50^{\circ}$
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Why The two base angles are equal and the angles sum to $180^{\circ}$, so each base angle is $\frac{180-40}{2}=70^{\circ}$.
8
Multiple choice · Easy
A cuboid measures $3$ cm by $4$ cm by $5$ cm. What is its volume?
$60$ cm$^{3}$
$12$ cm$^{3}$
$47$ cm$^{3}$
$94$ cm$^{3}$
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Why Volume of a cuboid $=length\times width\times height=3\times 4\times 5=60$ cm$^{3}$.
9
Multiple choice · Medium
What is the sum of the interior angles of a regular pentagon?
$540^{\circ}$
$360^{\circ}$
$108^{\circ}$
$720^{\circ}$
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Why Interior angle sum $=(n-2)\times 180=(5-2)\times 180=540^{\circ}$.
10
Multiple choice · Medium
A circle has radius $7$ cm. Using $\pi=3.14$, what is its area?
$153.86$ cm$^{2}$
$43.96$ cm$^{2}$
$21.98$ cm$^{2}$
$307.72$ cm$^{2}$
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Why Area $=\pi r^{2}=3.14\times 7^{2}=3.14\times 49=153.86$ cm$^{2}$. Using $2\pi r$ would give the circumference instead.
Key terms in Geometry and measures
Point: An exact position in space with no size, usually shown as a dot and labelled with a capital letter.
Line: A straight path that extends without end in both directions and has no thickness.
Line segment: A part of a line with two endpoints and a fixed length.
Ray: A part of a line with one endpoint that extends without end in one direction.
Angle: The amount of turn between two lines meeting at a point, measured in degrees.
Degree: A unit for measuring angles, where a full turn is $360$ degrees.
Acute angle: An angle smaller than $90$ degrees.
Right angle: An angle of exactly $90$ degrees, shown by a small square.
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