QUESTION 3
Easy
Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm.
SOLUTION
1
Write what is given
First side, \(a = 8\,cm\)
Second side, \(b = 11\,cm\)
Perimeter \(= 32\,cm\)
Second side, \(b = 11\,cm\)
Perimeter \(= 32\,cm\)
2
Find the third side
Third side, \(c = 32 − (8+11) = 13\,cm\)
3
Find the semi-perimeter \(s\)
\(s = \frac{32}{2} = 16\,cm\)
4
Find the area using Heron's formula
\(\begin{aligned} Area &= \sqrt{s(s−a)(s−b)(s−c)} \\ &= \sqrt{16(16−8)(16−11)(16−13)}\\ &= \sqrt{16 × 8 × 5 × 3} \\ &= \sqrt{1920} \\ &= \sqrt{64 × 30} \\ &= 8 \sqrt{30}\end{aligned}\)
Using \(\sqrt{30}\approx5.477\), we get
\(Area \approx8 × 5.477 \approx 43.8\) The area of the triangle is \(8\sqrt{30}\,cm\) or approximately 43.8 cm\(^2\).
Using \(\sqrt{30}\approx5.477\), we get
\(Area \approx8 × 5.477 \approx 43.8\) The area of the triangle is \(8\sqrt{30}\,cm\) or approximately 43.8 cm\(^2\).
Concept Note
When all three sides of a triangle are known, use Heron's formula to find the area, which is given by
\(Area = \sqrt{s(s−a)(s−b)(s−c)}\)
where,
\(s = \frac{a+b+c}{2}\) is the semi-perimeter.