How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 8 units in length?

Question

Elijah Alexander · Accepted Answer

≈ 11.62 square units

This method involves two steps. First, compute half of the perimeter's sum (s). #color(red)(|bar(ul(color(white)(a/a)color(black)(s=(a+b+c)/2)color(white)(a/a)|)))# Given that a = 6, b = 4, and c = 8 are the triangle's sides, #rArrs=(6+4+8)/2=18/2=9# Step 2: use to compute the area (A) #color(red)(|bar(ul(color(white)(a/a)color(black)(A=sqrt(s(s-a)(s-b)(s-c)))color(white)(a/a)|)))# #A=sqrt(9(9-6)(9-4)(9-8))# #=sqrt(9xx3xx5xx1)=sqrt135≈11.62 (2 "decimal places")#

Grace Ashcraft · Answer

undefined To use Heron's formula to determine the area of a triangle with sides of lengths 6, 4, and 8 units, you first calculate the semi-perimeter $ s $ using the formula:

$$ s = \frac{a + b + c}{2} $$

where $ a $, $ b $, and $ c $ are the lengths of the triangle's sides.

For this triangle:

$$ s = \frac{6 + 4 + 8}{2} = 9 $$

Next, you use Heron's formula to find the area ($ A $):

$$ A = \sqrt{s(s - a)(s - b)(s - c)} $$

where $ s $ is the semi-perimeter, and $ a $, $ b $, and $ c $ are the lengths of the sides.

Substituting the values:

$$ A = \sqrt{9(9 - 6)(9 - 4)(9 - 8)} $$

$$ A = \sqrt{9 \times 3 \times 5 \times 1} $$

$$ A = \sqrt{135} $$

$$ A \approx 11.618 $$

So, the area of the triangle is approximately 11.618 square units.