Question

find the area of this triangle.
155
175
260
area = ? units²
round to the nearest whole number.

Explanation:

Step1: Define sides for Heron's formula

Let $a=155$, $b=175$, $c=260$

Step2: Calculate semi-perimeter $s$

$s=\frac{a+b+c}{2}=\frac{155+175+260}{2}=\frac{590}{2}=295$

Step3: Apply Heron's formula

Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{295(295-155)(295-175)(295-260)}$
$=\sqrt{295\times140\times120\times35}$

Step4: Compute product inside root

$295\times140=41300$, $120\times35=4200$
$41300\times4200=173460000$

Step5: Calculate square root

$\sqrt{173460000}\approx13170.42$

Step6: Round to nearest whole number

Round $13170.42$ to $13170$

Answer:

13170 units²