Page 168 - MAT KS3 Y8 Cambridge CheckPoint

17.1 The area of a triangle

17.1 The area of a triangle surrounding
rectangle

The area of a triangle is always half of the area of the
rectangle that surrounds it, as these diagrams show.
You find the area of a rectangle by multiplying the base
by the height. So, the area of a triangle will be a half of the
base multiplied by the height. height
1
You can write the formula as: area = × base × height
2
1
or simply: A = bh base
2
Note that the height measurement of the triangle must be the
The height must be at right
perpendicular height, from the base to the opposite vertex.
angles (90°) to the base.

Worked example 17.1

a Work out the area of this triangle.
b Check your answer using estimation. 5.2 cm

9.8 cm

1 1
a A = bh = × 9.8 × 5.2 Write down the formula, then substitute the values of b and h.
2 2
= 25.48 cm Work out the answer. Remember to include the units (cm ).
2
2
b 5.2 → 5 and 9.8 → 10 First, round the base and height to the nearest whole number.
1
2
A = × 10 × 5 = 25 cm Use the rounded numbers to work out an estimate of the area.
2
25 is close to 25.48, so the accurate answer is probably correct.
Exercise 17.1

1 a Work out the areas of each triangle.
i ii iii
2.6 cm 7.9 cm 3.8 m

4.1 cm 12.2 cm 5.8 m
b Use estimation to check each answer in part a.

2 The length of the base of a triangle is 8.2 cm.
2
The area of the triangle is 39.77 cm .
Shen works out that the perpendicular height of the triangle is 7.9 cm.
a Without using a calculator, explain how you can tell that Shen is wrong.
39.77 cm 2
b Work out the perpendicular height of the triangle.
c What mistake do you think Shen made?
8.2 cm

166 17 Area, perimeter and volume
166