Question

area and perimeter of triangles
calculating area using herons formula
herons formula:
area = √(s(s - a)(s - b)(s - c))
use the triangle pictured to calculate the following measurements. then, calculate the area rounded to the nearest tenth using herons formula.
perimeter: p = units
semiperimeter: s = units
area: a ≈ square units

Explanation:

Step1: Calculate the perimeter

The perimeter $p$ of a triangle with side - lengths $a = 8$, $b = 10$, and $c = 12$ is $p=a + b + c$.
$p=8 + 10+12=30$

Step2: Calculate the semi - perimeter

The semi - perimeter $s=\frac{p}{2}$. Since $p = 30$, then $s=\frac{30}{2}=15$.

Step3: Calculate the area using Heron's formula

Heron's formula is $A=\sqrt{s(s - a)(s - b)(s - c)}$. Substitute $s = 15$, $a = 8$, $b = 10$, and $c = 12$ into the formula.
$A=\sqrt{15(15 - 8)(15 - 10)(15 - 12)}=\sqrt{15\times7\times5\times3}=\sqrt{1575}\approx39.7$

Answer:

Perimeter: $p = 30$ units
Semi - perimeter: $s = 15$ units
Area: $A\approx39.7$ square units