Chapter 11.1, Problem 12PPS

To determine

To calculate: To find the perimeter and area of each triangle.

Answer to Problem 12PPS

The area and perimeter of triangle is $137.5m{m}^2$ and $80mm$ respectively.

Explanation of Solution

Given information: The given figure in question.

Calculation:

For the area of triangle,

  $\begin{array}{l}\text{Area = }\frac{1}{2}\times \text{base }\times \text{ height}\\ \text{Area}=\frac{1}{2}\times 11\times 25\\ \text{Area}=\frac{1}{2}\times 275\\ \text{Area}=137.5m{m}^2\end{array}$

Use Pythagoras theorem to determine the length of third side of triangle,

  $\begin{array}{l}{a}^2+b^2=c^2\\ {25}^2+{23}^2=c^2\\ 625+529=c^2\\ 1154=c^2\\ \sqrt{1154}=c\\ 33.97mm=c\end{array}$

Now, for the perimeter of triangle,

  $\begin{array}{l}\text{Perimeter }=33.97+35+11\\ \text{Perimeter }=79.97mm\end{array}$

Rounding off to the nearest tenth, the perimeter of triangle is $80mm$