Measurement
Area of triangles and parallelograms
Find the area of a parallelogram, a triangle and a rhombus, and the perimeter of a straight-sided shape.
Perimeter is the distance all the way round a shape, measured in centimetres. Area is the amount of flat space inside it, measured in square centimetres. They answer different questions — how much fencing, and how much grass.
Height means upright
For a parallelogram, area = base × height, and for a triangle, area = 1/2 × base × height. In both, the height is measured straight up from the base at a right angle. It is almost never the slanting side, and using the slanting side by mistake is the commonest wrong answer in this whole topic.
Worked example
A parallelogram has a base of 8 cm and a height of 5 cm. What is its area?
Imagine cutting the slanting triangle off one end and sliding it round to the other.
Nothing is added or thrown away, so the area does not change — and what you are left with is a plain rectangle.
Try it together
Now a triangle with a base of 12 cm and a height of 5 cm.
Two identical triangles fit together into a parallelogram, so a triangle is always exactly half of one.
1.Start with the parallelogram that has the same base and height. What is 12 × 5?
Have a go
Have a go on your own: a parallelogram has a base of 7 cm and a height of 4 cm. What is its area, in square centimetres?
Hint: Base times height.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.