The area of the triangle is 96.1
STEP- BY - STEP EXPLANATION
What to find?
Area of the triangle ABC.
Given:
a = 13, b = 17, c = 26
To find the area of triangle ABC, follow the steps below:
Step 1
Since, the height of the triangle is not given, we will need to use Heron's formula.
Recall the Heron's formula below;
[tex]\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}[/tex]
Where P is half of the perimeter of the triangle.
a, b and c are the sides of the triangle.
Step 2
Find the value of P.
From the definition of p,
[tex]P=\frac{a+b+c}{2}[/tex][tex]\begin{gathered} P=\frac{13+17+26}{2} \\ \\ =\frac{56}{2} \\ \\ =28 \end{gathered}[/tex]
Step 3
Substitute the values into the Heron's formula.
[tex]\text{Area}=\sqrt[]{28(28-13)(28-17)(28-26)}[/tex]
Step 4
Simplify the resultant in step 3.
[tex]\begin{gathered} \text{Area}=\sqrt[]{28\times15\times11\times2} \\ \\ =\sqrt[]{9240} \\ \approx96.1 \end{gathered}[/tex]
Therefore, the area of the traingle is 96.1
