Find the area of a triangle ABC such that a = 16cm, b = 14cm, c = 12cm, leave your answer in surd form
a
5\(\sqrt{15}\)cm2
b
7\(\sqrt{15}\)cm2
c
21\(\sqrt{3}\)cm2
d
21\(\sqrt{5}\)cm2
e
21\(\sqrt{15}\)cm2
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Akosuah111
3 years ago
We can use Heron's formula to find the area of the triangle ABC, given the lengths of its sides:
Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
Substituting the values of a, b, and c, we get:
s = (16 + 14 + 12) / 2 = 21
Now, we can calculate the area using Heron's formula:
Area = √[21(21-16)(21-14)(21-12)]
= √[21(5)(7)(9)]
= √(21 * 5 * 7 * 9)
= √(5^2 * 3^2 * 7 * 3)
= 15√7 cm²
Therefore, the area of triangle ABC is 15√7 cm².
