# 11-Plus Maths Quiz - Perimeter and Area 2 (Medium) (Questions)

This is the second of our medium level Eleven Plus maths quizzes on perimeter and area. In the first, we looked at ways to work these out with different shapes – the rules for circles are quite different to the rules for rectangles!

• The formula for the area of a square is: Area = length2
• The formula for the area of a right-angle triangle is: Area = 12 × base × height
• The formula for the area of a circle is: Area = πr2
• The formula for the circumference of a circle is: Circumference = 2πr
• π = 227 or 3.142

And now it’s time to put all this to the test. Let’s see if you are a master of perimeter and area.

1. The surface area of a cube is 384 cm2. How tall is the cube?
 [ ] 8 cm [ ] 16 cm [ ] 32 cm [ ] 64 cm
2. A heptagon is a seven-sided shape. What is the perimeter of a regular heptagon if one of its sides is of length 19.3 cm?
 [ ] 372.49 cm [ ] 135.1 cm [ ] 115.8 cm [ ] 193 cm
3. The perimeter of a square is 28 cm. What is its area?
 [ ] 784 cm2 [ ] 196 cm2 [ ] 49 cm2 [ ] 7 cm2
4. The area of a wall is 12 m2. A can of paint can cover an area of 5 m2. How many cans of paint will be required to cover the wall?
 [ ] 1 [ ] 4 [ ] 2 [ ] 3
5. A right-angled triangle has a side length of 12 cm. How many of these triangles will fit onto a square whose sides are 28 cm long, without overlapping or going over the edge of the square?
 [ ] 10 [ ] 5 [ ] 15 [ ] 7
6. If the diameter of a circle is 14 cm, what is its circumference (assume that π = 3.142)?
 [ ] 138.21 cm [ ] 43.988 cm [ ] 87.976 cm [ ] 21.994 cm
7. The area of a right-angled triangle is 225 cm2. If its base is 15 cm, what is its height?
 [ ] 10 cm [ ] 20 cm [ ] 30 cm [ ] 40 cm
8. If you double the length of the sides of a square, what will happen to its area?
 [ ] It will stay the same [ ] It will double (multiply by 2) [ ] It will treble (multiply by 3) [ ] It will quadruple (multiply by 4)
9. If the circumference of a circle is 44 cm, what is its radius (assume that π = 3.142 and round your answer to the nearest whole number)?
 [ ] 7 cm [ ] 8 cm [ ] 9 cm [ ] 10 cm
10. If the diameter of a circle doubles, what will happen to the area?
 [ ] It will quintuple (multiply by 5) [ ] It will quadruple (multiply by 4) [ ] It will treble (multiply by 3) [ ] It will double (multiply by 2)
11-Plus Maths Quiz - Perimeter and Area 2 (Medium) (Answers)
1. The surface area of a cube is 384 cm2. How tall is the cube?
 [x] 8 cm [ ] 16 cm [ ] 32 cm [ ] 64 cm
A cube has six faces: each face is a square. So, to find the area of each face, divide 384 by 6:
384 ÷ 6 = 64. Next, we want to find the length of each square. The formula for the area of a square is: Area = length2.
If you know your times tables then you should know that 8 x 8 = 64
2. A heptagon is a seven-sided shape. What is the perimeter of a regular heptagon if one of its sides is of length 19.3 cm?
 [ ] 372.49 cm [x] 135.1 cm [ ] 115.8 cm [ ] 193 cm
A regular heptagon has ALL its sides the same length ∴ perimeter = 7 × 19.3 = 135.1 cm
3. The perimeter of a square is 28 cm. What is its area?
 [ ] 784 cm2 [ ] 196 cm2 [x] 49 cm2 [ ] 7 cm2
The perimeter of a square is 4 x its length. 28 ÷ 4 = 7
The area of a square is length x length. 7 x 7 = 49
4. The area of a wall is 12 m2. A can of paint can cover an area of 5 m2. How many cans of paint will be required to cover the wall?
 [ ] 1 [ ] 4 [ ] 2 [x] 3
12 ÷ 5 = 2.4. However, you cannot but 0.4 cans of paint – you would have to buy 3. Watch out for questions like this in exams – don’t let them trick you
5. A right-angled triangle has a side length of 12 cm. How many of these triangles will fit onto a square whose sides are 28 cm long, without overlapping or going over the edge of the square?
 [x] 10 [ ] 5 [ ] 15 [ ] 7
The area of square = 28 × 28 = 784 cm2.
Area of the triangles = 12 × base × height = 12 × 12 × 12 = 72 cm2.
The number of triangles = 784 ÷ 72 = 10.888. However, the question says, ‘without overlapping or going over the edge of the square’. This means that remainders are not counted. The answer is 10
6. If the diameter of a circle is 14 cm, what is its circumference (assume that π = 3.142)?
 [ ] 138.21 cm [x] 43.988 cm [ ] 87.976 cm [ ] 21.994 cm
The circumference of a circle = 2πr. As you know, diameter = 2r so part of this problem was already done for you
7. The area of a right-angled triangle is 225 cm2. If its base is 15 cm, what is its height?
 [ ] 10 cm [ ] 20 cm [x] 30 cm [ ] 40 cm
Area = (base × height) ÷ 2:
225 = (15 x height) ÷ 2:
2 x 225 ÷ 15 = height:
450 ÷ 15 = height = 30 cm
8. If you double the length of the sides of a square, what will happen to its area?
 [ ] It will stay the same [ ] It will double (multiply by 2) [ ] It will treble (multiply by 3) [x] It will quadruple (multiply by 4)
Suppose we have a square of side length 4 cm. Its area = 4 x 4 = 16 cm2
Now we double the length of its sides. Its area is now 8 x 8 = 64 cm2
64 ÷ 16 = 4. The area has quadrupled in size
9. If the circumference of a circle is 44 cm, what is its radius (assume that π = 3.142 and round your answer to the nearest whole number)?
 [x] 7 cm [ ] 8 cm [ ] 9 cm [ ] 10 cm
Circumference = 2πr, so 44 = 2 × 3.142 × r
We can rearrange the problem to, r = 44 ÷ (3.142 x 2):
So, r = 44 ÷ 6.284 = 7
10. If the diameter of a circle doubles, what will happen to the area?
 [ ] It will quintuple (multiply by 5) [x] It will quadruple (multiply by 4) [ ] It will treble (multiply by 3) [ ] It will double (multiply by 2)
As you know, diameter is twice radius. In circles, area = πr2. If r = 1 cm, A = 3.142 × 1 × 1 = 3.142 cm. Now, if r = 2, A = 3.142 × 2 × 2 = 12.568.
It’s not obvious at first but 12.568 is four times 3.142. Work it out and see for yourself.