The perimeter of an equilateral triangle is 12. Find the area to the nearest tenth
+33616 The area of a triangle can be obtained from Heron's formula:
\(Area = \sqrt{s(s-a)(s-b)(s-c)}\)
where a, b and c are the lengths of the sides and s = (a+b+c)/2
In this case a = b = c = 12/3 = 4 and s = 12/2 = 6 so
\(Area = \sqrt{6\times 2^3}=\sqrt{48}=4\sqrt3\)
I'll leave you to turn this into a decimal to the nearest tenth.
