**Perimeter and area when dealing with circular objects usually involves circumference.** This is the second 11-plus Maths quiz on perimeter and area. In this quiz we are going to have a look at a few different shapes.

The following symbols may be of use in doing this quiz:

- millimetre (mm); centimetre (cm); metre (m)
- square millimetre (mm
^{2}); square centimetre (cm^{2}); square metre (m^{2})

If you haven't played our easier quizzes yet, give them a go before tackling this one. Remember, take your time, read everything carefully and see if you can get top marks. Enjoy yourself!

1.

A nonagon is a nine-sided shape. What is the perimeter of a regular nonagon if one of its sides is of length 8 cm?

64 cm

81 cm

72 cm

96 cm

A regular nonagon has ALL its sides the same length ∴ perimeter = 9 × 8 = 72 cm

2.

A designer is making a pattern with right angled isosceles triangles. The sides that form the right angle in the right angled isosceles triangles are all of side length 6 cm. The designer has a selection of different coloured right angled isosceles triangles which he wishes to stick onto a square whose side length is 72 cm. How many of these coloured triangles will fit onto the square, without overlapping?

144

432

36

288

The area of square = 72 × 72 = 5,184 cm^{2}. Area of the triangle = ^{1}⁄_{2} × base × height = ^{1}⁄_{2} × 6 × 6 = 18 cm^{2}. The number of triangles = 5,184 ÷ 18 = 288. You have to divide 5,184 by 18 because you want to find out how many 'lots' of 18 there are in 5,184: each 'lot' equals one triangle: this is the same as adding 'lots' of 18 to itself until you get to 5,184. Incidentally, the triangles will fit because 72 is a multiple of 6: 12 × 6 = 72. There is another way of doing this problem: think about squares!

3.

If the radius of a circle is 7 cm, what is its circumference (take π = ^{22}⁄_{7})?

154 cm^{2}

44 cm^{2}

154 cm

44 cm

Circumference, C = 2πr = 2 × ^{22}⁄_{7} × 7 = 44 cm

4.

If you fold a square in half along an axis of symmetry parallel to one of its sides, the area will halve. If you fold the resulting shape in half again along an axis of symmetry parallel to one of its sides, what will happen to its area?

It will be the same as the original area

It will be an eighth of the original area

It will be a half of the original area

It will be a quarter of the original area

Suppose we have a square of side length 4 cm. Fold it in half along an axis of symmetry parallel to one of its sides: one side is now 4 cm and the other is 2 cm ∴ area = 2 × 4 = 8 cm^{2} = half of the original area of 16 cm^{2}. Now fold it in half along an axis of symmetry parallel to the 4 cm side: one side is now 4 cm and the other is 1 cm ∴ area = 1 × 4 = 4 cm^{2} = a quarter of the original area of 16 cm^{2}. The same is true if you fold it in half along an axis of symmetry parallel to the 2 cm side: try it!

5.

If the radius of a circle doubles, what will happen to the area?

There isn't enough information to answer the question

It will quadruple

It will double

It will treble

The area, A = πr^{2}. if r = 7 cm, A = ^{22}⁄_{7} × 7 × 7 = 154 cm. Now, if r = 14, A = ^{22}⁄_{7} × 14 × 14 = 616 cm^{2} = 4 times the original area. Although a specific example is not a proof, it can be shown that this will always happen: if you double the radius, the area will quadruple

6.

The area of a rectangle is 150 cm^{2}. If one side is 50 cm, what is the length of the other side?

3 cm

3 cm^{2}

3 mm

3 mm^{2}

Area = length × width ∴ 150 = 50 × 3. Make sure that you USE the UNITS RIGHT!

7.

If the radius of a circle doubles, what will happen to the circumference?

It will double

Nothing

It will halve

There isn't enough information to answer the question

The circumference, C = 2πr. If you double the radius r, then it becomes 2r. Now C = 4πr = twice the original circumference. If you have difficulty in seeing this, try this example, if r = 7 cm, C = 44 cm. If r = 14 cm, C = 88 cm. Use π = ^{22}⁄_{7}

8.

What is the surface area of a cube of side length 10 mm?

600 cm^{2}

60 mm^{2}

600 mm^{2}

60 cm^{2}

A cube has six faces: each face is a square. In this case, each square has a side length of 10 mm, so the area = 10 × 10 = 100 mm^{2}. Each square makes up the face of the cube, so surface area of a cube = 6 × 100 mm^{2} = 600 mm^{2}

9.

The area of a floor is 25 m^{2}. The floor is to be tiled with tiles whose area is 0.25 m^{2}. How many tiles will be required?

500

250

100

200

The number of tiles = 25 ÷ 0.25 = 100. You have to divide 25 by 0.25 because you want to find out how many 'lots' of 0.25 there are in 25: each 'lot' equals one tile: this is the same as adding 'lots' of 0.25 to itself until you get to 25. By the way, 0.25 =^{1}⁄_{4}. To divide by a fraction, invert and multiply: 4 × 25 = 100

10.

The circumference of a circle of radius 7 cm is 44 cm. If the circle is cut in half, what is the length of the perimeter of one of the half circles?

36 cm

22 cm

14 cm

44 cm

If the circle is cut in half, the length of the perimeter of one of the half circles = the perimeter of the semi-circle + the length of the diameter of the circle = 22 + 14 = 36 cm