So, you have made it to the third in our difficult series of Eleven Plus maths quizzes on perimeter and area – give yourself a pat on the back for making it this far! In your exam you will have to work out the perimeter and area of 2D shapes, like squares, along with the surface area and volume of 3D shapes, like cubes. This quiz will help you practice.

While we are on the subject of shapes, here are the names of some lesser-known ones:

- Triangle: 3 sides
- Quadrilateral: 4 sides
- Pentagon: 5 sides
- Hexagon: 6 sides
- Heptagon: 7 sides
- Octagon: 8 sides
- Nonagon: 9 sides
- Decagon: 10 sides
- Hendecagon: 11 sides
- Dodecagon: 12 sides

Don’t worry – you won’t need to know all of these - but if you can remember them all, they may come in useful at some point.

1.

What do we call the longest side of a right-angled triangle?

The scalene

The isosceles

The hypotenuse

The equilateral

It’s the side opposite the right-angle

2.

A right-angle triangle has a base of 16 cm and a height of 12 cm. What is its area?

192 cm^{2}

96 cm^{2}

146 cm^{2}

73 cm^{2}

The area of a right-angle triangle = (base × height) ÷ 2.

(16 x 12) ÷ 2 = 192 ÷ 2 = 96 cm^{2}

(16 x 12) ÷ 2 = 192 ÷ 2 = 96 cm

3.

Circle A has a radius of 10 cm and a circumference of 63 cm. If it is cut into two equal sized semicircles, what is the circumference of one of those semicircles?

51.5 cm

41.5 cm

31.5 cm

21.5 cm

If you cut a circle into two semicircles their circumference will be half the circle’s circumference + the circle’s diameter (radius x 2).

(63 ÷ 2) + (10 x 2) = 31.5 + 20 = 51.5 cm

(63 ÷ 2) + (10 x 2) = 31.5 + 20 = 51.5 cm

4.

Circle A has an area of 64 cm^{2}. Circle B has a radius a quarter the size of Circle A’s radius. What is the area of circle B?

16 cm^{2}

24 cm^{2}

32 cm^{2}

48 cm^{2}

If you double the area of a circle, the radius is decreased fourfold (divided by 4). Conversely, if you decrease the radius of a circle by dividing it by 4, the area is halved

5.

What is the area of a circle whose diameter = 20 cm (take pi to be 3.142)?

1,256.8 cm^{2}

314.2 cm^{2}

125.6 cm^{2}

31.42 cm^{2}

The formula for the area of a circle is πr^{2}. As you know, the radius is half the diameter, so the area of this circle will be:

3.142 x (20 ÷ 2)^{2} =

3.142 x 10^{2}

3.142 x 100 = 314.2 cm^{2}

3.142 x (20 ÷ 2)

3.142 x 10

3.142 x 100 = 314.2 cm

6.

A regular decagon has sides measuring 7 cm each. What is its perimeter?

70 cm

63 cm

56 cm

49 cm

The length of the perimeter of a regular polygon is found by multiplying the length of one of its sides by the number of sides. Decagons have ten sides, so 7 x 10 = 70 cm

7.

The height of a cube is 4 cm. What is its total surface area?

32 cm^{2}

64 cm^{2}

96 cm^{2}

3D shapes do not have area

3D shapes do have an area, which we call 'surface area'.

A cube has six faces, each of which is a square, so to find its surface are we work out the area of one face and then multiply by 6

4 x 4 x 6 = 96 cm^{2}

A cube has six faces, each of which is a square, so to find its surface are we work out the area of one face and then multiply by 6

4 x 4 x 6 = 96 cm

8.

A cube has a height of 2 cm. What is its volume?

24 cm^{3}

8 cm^{2}

8 cm^{3}

6 cm^{3}

The volume of a cube = length^{3}:

2 x 2 x 2 = 8 cm^{3}.

Make sure you don’t confuse cubed with squared!

2 x 2 x 2 = 8 cm

Make sure you don’t confuse cubed with squared!

9.

A cuboid has a height of 5 cm. What is its surface area?

150 cm^{2}

125 cm^{2}

100 cm^{2}

Not enough information to answer the question

The surface area of a cube = height x height x 6 (because it has 6 faces). However, the surface area of a cuboid is length x height x 6. We do not know the length of this cuboid, so we cannot answer the question.

Make sure you don’t confuse cuboids with cubes!

Make sure you don’t confuse cuboids with cubes!

10.

Square A has an area of 25 cm^{2}. Square B is twice as wide as square A. What is the area of square B?

50 cm^{3}

75 cm^{3}

100 cm^{3}

125 cm^{3}

If you double the width of a square, its area quadruples (times by 4). Here’s the proof:

Square A: 5 x 5 = 25

Square B: 10 x 10 = 100

Square A: 5 x 5 = 25

Square B: 10 x 10 = 100