How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 4 units in length?

Question

Nolan Alexander · Accepted Answer

Area ≈ 7.94 This procedure has two steps. Step 1: Determine half of the triangle's perimeter (s). Secondly, compute the area (A). Assume a = 6, b = 4, and c = 4. step 1 : s = #(a + b + c )/2 = (6 + 4 + 4 )/2 = 14/2 = 7# step 2 : A# = sqrt(s(s-a)(s-b)(s-c))# # = sqrt(7(7-6)(7-4)(7-4)) # # = sqrt(7 xx 1 xx 3 xx 3) = sqrt63 ≈ 7.94#

Dylan Arnold · Answer

undefined To use Heron's formula to determine the area of a triangle with sides of lengths 6, 4, and 4 units, follow these steps:

1. Calculate the semi-perimeter ($s$) of the triangle using the formula:
$$ s = \frac{a + b + c}{2} $$
where $a$, $b$, and $c$ are the lengths of the sides of the triangle.

2. Compute the expression inside the square root of Heron's formula:
$$ A = \sqrt{s(s - a)(s - b)(s - c)} $$
where $s$ is the semi-perimeter, and $a$, $b$, and $c$ are the lengths of the sides of the triangle.

3. Substitute the given side lengths $a = 6$, $b = 4$, and $c = 4$ into the formulas.

4. Calculate the semi-perimeter:
$$ s = \frac{6 + 4 + 4}{2} = 7 $$

5. Compute the expression inside the square root:
$$ A = \sqrt{7(7 - 6)(7 - 4)(7 - 4)} $$
$$ A = \sqrt{7(1)(3)(3)} $$
$$ A = \sqrt{63} $$

6. Simplify the square root:
$$ A = \sqrt{9 \times 7} $$
$$ A = 3\sqrt{7} $$

Therefore, the area of the triangle is $3\sqrt{7}$ square units.