Level 5-6 Shapes - Perimeter and Area
Here is an impossible triangle - just for fun.

Level 5-6 Shapes - Perimeter and Area

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!

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
Is a square also a rectangle?
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
If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its area?
49 cm2
121 cm2
77 cm2
It is impossible to say
The formula for calculating the area of a parallelogram is A = bh (Area = base x height)
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!
What is the area of a triangle that has a base of 37 cm and a perpendicular height of 28 cm?
518 cm2
1,063 cm2
1,360 cm2
1,630 cm2
Area of a triangle = 12(b x h)
If the area of a triangle is 420 cm2 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
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 cm2
200 cm2
225 cm2
250 cm2
Area of a trapezium = 12 (a + b)h
A garden is in the shape of a trapezium and it has an area of 1,500 metres2. 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
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?
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
If a rhombus has a base of 1.2 metres and a perpendicular height of 0.8 metres, what is its area?
0.64 m2
0.80 m2
0.96 m2
1.44 m2
Area of a rhombus = perpendicular height x side length
You can find more about this topic by visiting BBC Bitesize - Perimeter, Area, Volume

Author:  Frank Evans

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