As part of your work on shapes in KS3 Maths, you'll be very familiar with both perimeter and area. The perimeter is the total distance around the outside of a two-dimensional shape. The area is the amount of space covered by the shape's surface. To work out the area of a rectangle multiply the length of its longest side by the length of its shortest side. To work out its perimeter just add together the length of all of its sides.

So, you are fine with squares and oblongs. You might also be confident with triangles. But can you work out the perimeter and area of shapes such as a trapezium and a rhombus? They have their own rules which it will do you good to learn. The following quiz provides a more advanced look at calculating areas and perimeters of 2-Dimensional shapes.

Before trying this quiz, you might want to refresh your memory by playing the easier quiz called 'Level 3-4 Perimeter and Area 01'. Or, if you are already quite confident, then jump right on in. Good luck!

1.

The two parallel sides of a trapezium have lengths 10 cm and 20 cm, and the distance between them is 15 cm. What is the area of this trapezium?

150 cm^{2}

200 cm^{2}

225 cm^{2}

250 cm^{2}

2.

If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its perimeter?

44 cm

28 cm

36 cm

It is impossible to say

Did you get it wrong by confusing the perpendicular height with the length of its shortest side? The perpendicular height is NOT the same as the length of the shortest side!

3.

If the area of a triangle is 420 cm^{2} and its perpendicular height is 30 cm, what is the length of its base?

24 cm

26 cm

28 cm

32 cm

To find the area of a triangle, multiply the base by the height, and then divide by 2. So, to find the length of the base, divide 420 by 30 then multiply your answer by 2

4.

What is the area of a triangle that has a base of 37 cm and a perpendicular height of 28 cm?

518 cm^{2}

1,063 cm^{2}

1,360 cm^{2}

1,630 cm^{2}

Area of a triangle = ^{1}⁄_{2}(b x h)

5.

If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its area?

49 cm^{2}

121 cm^{2}

77 cm^{2}

It is impossible to say

The formula for calculating the area of a parallelogram is A = bh (Area = base x height)

6.

Is a square also a rectangle?

Yes

No

It depends on the length of its sides

It depends on its surface area

A square is a special rectangle - its length and width are the same

7.

A garden is in the shape of a trapezium and it has an area of 1,500 metres^{2}. One of the parallel sides is 40 metres long and the other parallel side is 60 metres long. What is the distance between the parallel sides?

20 metres

30 metres

40 metres

50 metres

When you are dealing with shapes it is often useful to draw the shape so that you can understand the question better

8.

In many formulas you will see the letter h which stands for 'height'. What would be a more correct term for 'height'?

Perpendicular height

Perpetrator height

Perpetual height

Perplexing height

The perpendicular height of an object should not be confused with the length of its shortest side

9.

If a rhombus has a base of 1.2 metres and a perpendicular height of 0.8 metres, what is its area?

0.64 m^{2}

0.80 m^{2}

0.96 m^{2}

1.44 m^{2}

Area of a rhombus = perpendicular height x side length

10.

Archie says that the area of a rhombus of side length 12 cm is the same as that of a square of side 12 cm. Is he right?

Always

Never

Sometimes - it depends on the size of the internal angles

Only if the perimeter is equal to 48cm

If the rhombus has a right angle, it is also a square

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^{1}⁄_{2}(a + b)h