Chapter 9.6, Problem 11PSA

To determine

To Calculate: The perimeter and area of $\Delta ABC$

Answer to Problem 11PSA

The perimeter and area are $40$ and $44$

Explanation of Solution

Given information:

Coordinates of A , B and C are $\left(-4,3\right),(11,3)$ and $\left(11,11\right)$

Formula used

Here, we are using distance formula.

Calculation:

Here, the formula is

Distance = $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

  →$AC=\sqrt{{\left(11+4\right)}^2+{\left(11-3\right)}^2}$

  →$AC=\sqrt{225+64}$

  →$AC=17$

And, $AB=\sqrt{{\left(11+4\right)}^2}$

  →$AB=\sqrt{225}$

  →$AB=15$

And, $CB=\sqrt{{\left(11-3\right)}^2}$

  →$CB=\sqrt{64}$

  →$CB=8$

Perimeter = $17+15+8=40$

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

  →$\frac{1}{2}\left|-4\left(0\right)+11\left(8\right)+11\left(0\right)\right|$

  →$\frac{1}{2}\times 88$

  →$44$

Conclusion: Hence,the perimeter and area are $40$ and $44$