Use Heron’s Area Formula to find the area of the triangle with the given measures.?

Question

Equilateral triange with a perimeter of 21.3

Answer 1

The Area of a equilateral triangle with L=side is A=(1/4)L^2sqrt3,
P=21,3m => L=P/3=7.1m =>A=(1/4)7.1^2sqrt3 m^2. END!

Answer 2

Heron's formula computes the area of a triangle given the length of each of the three sides. For an equilateral triangle:

a = b = c = 21.3/3 = 7.1

Let s = semi-perimeter of triangle.

Then s = (a + b + c)/2 = 21.3 / 2 = 10.65

Heron's formula for the area A of a triangle is:

A = √[s(s-a)(s-b)(s-c)] = √[10.65(10.65-7.1)^3]
= √[10.65(3.55)^3] = 21.82817

Checking the result with the usual formula for the area of an equilateral triangle.

A = (1/2)bh = (1/2)b[(√3/2)b = (√3/4)b^2
= (√3/4)(7.1)^2 = 21.82817

So the formulas agree.

Answer 3

Heron's formula is:

Area = square root [s(s-a)(s-b)(s-c)]

where a,b,and c are the lengths of the sides, and s is half the perimeter of the triangle.

An equilateral traingle with perimeter 21.3 has all three sides equal to (21.3)/3 = 7.1, so a = b = c = 7.1.

s = (21.3)/2 = 10.65

So,
A = square root [(10.65)(3.55)(3.55)(3.55)] = 21.83 units.
(rounded to two decimal places)

The exact answer would be 12.6025 sqrt(3)