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Maths Quiz - Perimeter and Area 3 (Difficult) (Questions)

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:

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. 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
2. A right-angle triangle has a base of 16 cm and a height of 12 cm. What is its area?
[ ] 192 cm2
[ ] 96 cm2
[ ] 146 cm2
[ ] 73 cm2
3. The height of a cube is 4 cm. What is its total surface area?
[ ] 32 cm2
[ ] 64 cm2
[ ] 96 cm2
[ ] 3D shapes do not have area
4. Circle A has an area of 64 cm2. Circle B has a radius a quarter the size of Circle A’s radius. What is the area of circle B?
[ ] 16 cm2
[ ] 24 cm2
[ ] 32 cm2
[ ] 48 cm2
5. A cuboid has a height of 5 cm. What is its surface area?
[ ] 150 cm2
[ ] 125 cm2
[ ] 100 cm2
[ ] Not enough information to answer the question
6. A regular decagon has sides measuring 7 cm each. What is its perimeter?
[ ] 70 cm
[ ] 63 cm
[ ] 56 cm
[ ] 49 cm
7. A cube has a height of 2 cm. What is its volume?
[ ] 24 cm3
[ ] 8 cm2
[ ] 8 cm3
[ ] 6 cm3
8. Square A has an area of 25 cm2. Square B is twice as wide as square A. What is the area of square B?
[ ] 50 cm2
[ ] 75 cm2
[ ] 100 cm2
[ ] 125 cm2
9. What is the area of a circle whose diameter = 20 cm (take pi to be 3.142)?
[ ] 1,256.8 cm2
[ ] 314.2 cm2
[ ] 125.6 cm2
[ ] 31.42 cm2
10. What do we call the longest side of a right-angled triangle?
[ ] The scalene
[ ] The isosceles
[ ] The hypotenuse
[ ] The equilateral
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Maths Quiz - Perimeter and Area 3 (Difficult) (Answers)
1. 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?
[x] 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
2. A right-angle triangle has a base of 16 cm and a height of 12 cm. What is its area?
[ ] 192 cm2
[x] 96 cm2
[ ] 146 cm2
[ ] 73 cm2
The area of a right-angle triangle = (base × height) ÷ 2.
(16 x 12) ÷ 2 = 192 ÷ 2 = 96 cm2
3. The height of a cube is 4 cm. What is its total surface area?
[ ] 32 cm2
[ ] 64 cm2
[x] 96 cm2
[ ] 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 cm2
4. Circle A has an area of 64 cm2. Circle B has a radius a quarter the size of Circle A’s radius. What is the area of circle B?
[ ] 16 cm2
[ ] 24 cm2
[x] 32 cm2
[ ] 48 cm2
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. A cuboid has a height of 5 cm. What is its surface area?
[ ] 150 cm2
[ ] 125 cm2
[ ] 100 cm2
[x] 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!
6. A regular decagon has sides measuring 7 cm each. What is its perimeter?
[x] 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. A cube has a height of 2 cm. What is its volume?
[ ] 24 cm3
[ ] 8 cm2
[x] 8 cm3
[ ] 6 cm3
The volume of a cube = length3:
2 x 2 x 2 = 8 cm3.
Make sure you don’t confuse cubed with squared!
8. Square A has an area of 25 cm2. Square B is twice as wide as square A. What is the area of square B?
[ ] 50 cm2
[ ] 75 cm2
[x] 100 cm2
[ ] 125 cm2
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
9. What is the area of a circle whose diameter = 20 cm (take pi to be 3.142)?
[ ] 1,256.8 cm2
[x] 314.2 cm2
[ ] 125.6 cm2
[ ] 31.42 cm2
The formula for the area of a circle is ?r2. 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 102
3.142 x 100 = 314.2 cm2
10. What do we call the longest side of a right-angled triangle?
[ ] The scalene
[ ] The isosceles
[x] The hypotenuse
[ ] The equilateral
It’s the side opposite the right-angle
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