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!
Here’s some information which might help you in the quiz:
And now it’s time to put all this to the test. Let’s see if you are a master of perimeter and area.















A regular heptagon has ALL its sides the same length ∴ perimeter = 7 × 19.3 = 135.1 cm


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 
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


The area of square = 28 × 28 = 784 cm^{2}.
Area of the triangles = ^{1}⁄_{2} × base × height = ^{1}⁄_{2} × 12 × 12 = 72 cm^{2}. 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 
The circumference of a circle = 2πr. As you know, diameter = 2r so part of this problem was already done for you


Area = (base × height) ÷ 2:
225 = (15 x height) ÷ 2: 2 x 225 ÷ 15 = height: 450 ÷ 15 = height = 30 cm 
Suppose we have a square of side length 4 cm. Its area = 4 x 4 = 16 cm^{2}
Now we double the length of its sides. Its area is now 8 x 8 = 64 cm^{2} 64 ÷ 16 = 4. The area has quadrupled in size 

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 
As you know, diameter is twice radius. In circles, area = πr^{2}. 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. 
384 ÷ 6 = 64. Next, we want to find the length of each square. The formula for the area of a square is: Area = length^{2}.
If you know your times tables then you should know that 8 x 8 = 64