Chapter 11.1, Problem 37HP

To determine

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

Answer to Problem 37HP

The answer is 15square units.

Explanation of Solution

Given information: Given coordinates are $A(-3,0),B(1,3)\text{and}C(3,-3)$

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 the given coordinates are $A(-3,0),B(1,3)\text{and}C(3,-3)$

Thus,

  $\begin{array}{l}\text{Area}\text{of}\Delta \text{ABC}\\ =\frac{1}{2}\times \left|y_1(x_2-x_3)+y_2(x_3-x_1)+y_3(x_1-x_2)\right|\\ =\frac{1}{2}\times \left|0(1-3)+3(3+3)-3(-3-1)\right|\\ =\frac{1}{2}\times \left|0+18+12\right|\\ =\frac{1}{2}\times 30\\ =15\end{array}$

Hence, the required area is 15 square units.