Chapter 11.1, Problem 34PPS

To determine

To Find: To find the area of the given figure.

Answer to Problem 34PPS

The answer is 3square units.

Explanation of Solution

Given information: Given coordinates are $R(-8,-2),S(-2,-2),\text{and}T(-3,-7)$

Formula used: Area of triangle $=\frac{1}{2}\times \left|y_1(x_2-x_1)+y_2(x_3-x_1)+y_3(x_1-x_2)\right|$

Calculation:

Since given coordinates are $R(-8,-2),S(-2,-2),\text{and}T(-3,-7)$

Thus,

  $\begin{array}{l}\text{Area}\text{of}\Delta RST\\ =\frac{1}{2}\times \left|y_1(x_2-x_3)+y_2(x_3-x_1)+y_3(x_1-x_2)\right|\\ =\frac{1}{2}\times \left|-2(-2+3)-2(-3+8)-3(-8+2)\right|\\ =\frac{1}{2}\times \left|-2-10+18\right|\\ =\frac{1}{2}\times 6\\ =3\end{array}$

Hence, the required area is 3 square units.