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Perimeter and Area 3 (Medium)
Welcome to the third in our Medium Difficulty series of Eleven Plus maths quizzes on perimeter and area. If you have played our previous quizzes, then you should be familiar with some of the formulae we use to work out the perimeter and area of 2D shapes. Here we’ll give you more practice, and throw in the odd 3D shape as well.
When dealing with circles, you will need to use π (pi). This is a mathematical constant used to calculate the circumference and the area of circles. Do you know its value? Some people can recite it to hundreds of decimal places, but three is generally enough!
Here’s pi to 100 decimal places, just in case you'd like to memorise it:
3.141592653589793238462643383279502884197169399375105820974
9445923078164062862089986280348253421170679
Because pi is an unusual number, you may want to use your calculator in this quiz. If so, don’t use the button marked π. Any questions you need pi for will tell you the value to use.
Now for the quiz – good luck!
We can rearrange the problem to, r = 19 ÷ (3.142 x 2):
So, r = 19 ÷ 6.284 = 3.024 which we round down to 3 cm
The perimeter of a square is 4 x its length. 8 x 4 = 32
Diameter is twice radius. In circles, area = ?r2. 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.
54 ÷ 6 = 9. 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 3 x 3 = 9
Next we divide 10,000 by 400 to find how many tiles are needed to cover one square metre: 10,000 ÷ 400 = 25
If it takes 25 tiles to cover 1 m2, then it will take 25 x 8 to cover 8 m2: 25 x 8 = 200
Jane will need 200 tiles – as long as she doesn’t break any that is!
Suppose we have a square of side length 2 cm. Its area = 2 x 2 = 4 cm2
Now we double the length of its sides. Its area is now 4 x 4 = 16 cm2
16 ÷ 4 = 4. The area has quadrupled in size
108 = (12 x height) ÷ 2:
2 x 108 ÷ 12 = height:
216 ÷ 12 = height = 18 cm
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? x 102 = 3.142 x 100 = 314.2 cm2