Chapter 16, Problem 12RP

To determine

To find: the area of triangle with having given three vertices.

Answer to Problem 12RP

  $55.5\text{ sq unit}\text{.}$

Explanation of Solution

Given:

  $\left(5,1\right),\left(16,-4\right)\text{ and }\left(3,12\right).$ .

Concept used:

Area of triangle having vertices:

  $\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$ .

Calculation:

According to the given the three vertices of the triangle are:

  $\left(5,1\right),\left(16,-4\right)\text{ and }\left(3,12\right).$

The area of triangle from the three vertices of the triangle is:

  $\begin{array}{l}\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|.\\ \Rightarrow \frac{1}{2}\left|5\left(-4-12\right)+16\left(12-1\right)+3\left(1-\left(-4\right)\right)\right|.\\ \Rightarrow \frac{111}{2}=\mathrm{55.5.}\end{array}$

Hence, the area of the triangle $55.5\text{ sq unit}\text{.}$