Page 169 - MAT KS3 Y8 Cambridge CheckPoint

17.2 The areas of a parallelogram and trapezium

17.2 The areas of a parallelogram and trapezium

Look at this parallelogram.
Imagine you cut off the triangle from the left end of
the parallelogram and moved it to the right end. You
would have made a rectangle.
So the area of the parallelogram is the same as the area of the
rectangle with the same base and height.
You can write the formula for the area of a parallelogram as:
height
area = base × height
base
or simply A = bh
Note that the height measurement of the parallelogram must be the perpendicular height.
Now look at this trapezium. a
The lengths of its parallel sides are a and b.
h
Its perpendicular height is h.
Two trapezia can be put together like this to make b
a parallelogram with a base length of (a + b) and a height h.
The area of the parallelogram is: h
area = base × height = (a + b) × h
a + b
The area of one trapezium is half the area of the parallelogram.
‘Trapezia’ is the plural of
1
So, the area of a trapezium is: A = × (a + b) × h
2 trapezium.
Note again, that the height measurement of the trapezium must be the
perpendicular height.

Worked example 17.2

Work out the area of each shape. a b 12 mm
5 cm
8 mm

7 cm
18 mm

a A = bh = 7 × 5 Write down the formula, then substitute for b and h.
2
2
= 35 cm Work out the answer, and remember to include the units (cm ).
1
b A = × (a + b) × h Write down the formula.
2
1
= × (12 + 18) × 8 Substitute the values of a, b and h.
2
1 1
= × 30 × 8 Work out 12 + 18 = 30 first, then work out of 30 = 15.
2 2
= 15 × 8 Finally work out 15 × 8.
2
2
= 120 mm Remember to include the units (mm ) with your answer.

17 Area, perimeter and volume 167