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 area of a square whose sides are 1 metre long?

1 m^{2}

10,000 cm^{2}

1 million mm^{2}

All of the above

2.

How many square millimetres are there in 1 m^{2}?

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 m^{2} = 1,000 x 1000 mm^{2}

1,000 x 1,000 = 1 million

There are 1,000 millimetres in 1 metre, so 1 m

1,000 x 1,000 = 1 million

3.

Two right-angled triangles, when put together, make a square with and area of 36 cm^{2}. 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 cm^{2}, its sides will be 6 cm long: 6 x 6 = 36

If the square has an area of 36 cm

4.

A square has an area of 120 cm^{2}. If it is cut from corner to corner into four right-angled triangles, what is the area of each triangle?

60 cm^{2}

40 cm^{2}

30 cm^{2}

20 cm^{2}

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

120 ÷ 4 = 30

5.

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!

6.

What is the formula for finding the area of a right-angled triangle?

Area = base × height

Area = ^{1}⁄_{2} × base × height

Area = ^{1}⁄_{2} × base × height^{2}

Area = ^{1}⁄_{4} × base × height

A right-angled triangle is half a rectangle, so the formula is the same as that for a rectangle, halved

7.

A square has an area of 144 cm^{2}. 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 cm^{2} = length × length. If you know your times tables you will know that 12 x 12 = 144

144 cm

8.

What is the formula for finding the area of a circle?

Area = π × r^{2}

Area = 2π × r

Area = π × r^{3}

Area = (π × r)^{2}

Learn this fact! It's the radius that is squared, not π × radius

9.

A rectangle has a length of 8 cm and a width of 2 cm. What is its area in mm^{2}?

16 mm^{2}

16 cm^{2}

160 mm^{2}

1,600 mm^{2}

The area of a rectangle = length x width:

8 x 2 = 16

There are 100 mm^{2} in one cm^{2} so 16 x 100 = 1,600

8 x 2 = 16

There are 100 mm

10.

What is the formula for finding the circumference of a circle?

Circumference = 2π x diameter

Circumference = π x diameter

Circumference = π x radius

Circumference = π x radius^{2}

Another way to say this is circumference = π x (radius x 2) because the diameter is twice the radius

^{2}100 x 100 = 10,000, so 1 metre is 10,000 cm

^{2}1,000 x 1,000 = 1 million, so 1 metre is 1 million mm

^{2}