Question

Find the area of the triangle.Triangle ABC , a = 13, b = 17, c = 26Round to one decimal.

Answer 1

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;

`\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}`

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,

`P=(a+b+c)/(2)`
`\begin{gathered} P=(13+17+26)/(2) \\ \\ =(56)/(2) \\ \\ =28 \end{gathered}`

Step 3

Substitute the values into the Heron's formula.

`\text{Area}=\sqrt[]{28(28-13)(28-17)(28-26)}`

Step 4

Simplify the resultant in step 3.

`\begin{gathered} \text{Area}=\sqrt[]{28*15*11*2} \\ \\ =\sqrt[]{9240} \\ \approx96.1 \end{gathered}`

Therefore, the area of the traingle is 96.1