The lengths of the three sides of a triangular field are 15 m, 19 m and 22 m respectively. What is the area of the field? (correct to one decimal place)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 140.2 m2
When all three sides are known, the area comes from Heron’s formula, \(\sqrt{s(s-a)(s-b)(s-c)}\), where \(s\) is the semi-perimeter.
Semi-perimeter: \(\displaystyle s=\frac{15+19+22}{2}=28\)
Differences from the three sides: \(s-a=13\), \(s-b=9\), \(s-c=6\)
Area \(=\sqrt{28\times13\times9\times6}=\sqrt{19656}\)
\(140^{2}=19600\) and \(140.2^{2}\approx19656\), so the area is about 140.2 m2