 There are 1 million mm2 in 1 m2.

# Perimeter and Area 3 (Easy)

Welcome to the third of our Easy level Eleven Plus maths quizzes on Perimeter and Area. In the previous quizzes we learned some formulae (that’s the plural of formula) to calculate the area and the perimeter of 2D (2 dimensional) shapes, like circles and squares. In this quiz we go over what we have learned already and give you a recap of those formulae.

The perimeter is the total length of all the sides of a shape. In circles, we call the perimeter the circumference.

The area is the amount of space taken up by a 2D shape. The way it is calculated is different in circles and squares. Can you remember the formulae? If not, don’t worry. The helpful comments which follow each question will explain anything you need to know.

So now it’s time for the quiz. Be sure to read each question thoroughly and to think about your answers. Some of the questions may have appeared in previous quizzes – that’s intentional. The more often you go over a fact, the more likely you are to remember it when your exams come along.

1.
What is the formula for calculating the perimeter of a rectangle?
Perimeter = (2 × length) + (2 × width)
Perimeter = length + width
Perimeter = 4 × length
Perimeter = length × width
Do not confuse perimeter and area!
2.
What is the formula for finding the circumference of a circle?
Circumference = 2π x diameter
Circumference = π x diameter
Another way to say this is circumference = π x (radius x 2) because the diameter is twice the radius
3.
What is the area of a square whose sides are 1 metre long?
1 m2
10,000 cm2
1 million mm2
All of the above
1 x 1 = 1, so 1 metre is 1 m2
100 x 100 = 10,000, so 1 metre is 10,000 cm2
1,000 x 1,000 = 1 million, so 1 metre is 1 million mm2
4.
What is the formula for finding the area of a right-angled triangle?
Area = base × height
Area = 12 × base × height
Area = 12 × base × height2
Area = 14 × base × height
A right-angled triangle is half a rectangle, so the formula is the same as that for a rectangle, halved
5.
A rectangle has a length of 8 cm and a width of 2 cm. What is its area in mm2?
16 mm2
16 cm2
160 mm2
1,600 mm2
The area of a rectangle = length x width:
8 x 2 = 16
There are 100 mm2 in one cm2 so 16 x 100 = 1,600
6.
How many square millimetres are there in 1 m2?
10,000
10,000
100,000
1 million
The area of a square = length x length:
There are 1,000 millimetres in 1 metre, so 1 m2 = 1,000 x 1000 mm2
1,000 x 1,000 = 1 million
7.
What is the formula for finding the area of a circle?
Area = π × r2
Area = 2π × r
Area = π × r3
Area = (π × r)2
Learn this fact! It's the radius that is squared, not π × radius
8.
A square has an area of 120 cm2. If it is cut from corner to corner into four right-angled triangles, what is the area of each triangle?
60 cm2
40 cm2
30 cm2
20 cm2
If a square is made up of 4 right-angled triangles, then just divide the area of the square by four to find the answer:
120 ÷ 4 = 30
9.
Two right-angled triangles, when put together, make a square with and area of 36 cm2. What is the length of the base of each triangle (not the diagonal side)?
24 cm
18 cm
12 cm
6 cm
If two right angled triangles form a square, then the length of their bases will be equal to the length of the square’s sides.
If the square has an area of 36 cm2, its sides will be 6 cm long: 6 x 6 = 36
10.
A square has an area of 144 cm2. What is the length of the square’s sides?
12 cm
14 cm
24 cm
28 cm
The area of a square = length × length:
144 cm2 = length × length. If you know your times tables you will know that 12 x 12 = 144
Author:  Frank Evans