Chapter 1.2, Problem 36PPS

To determine

To Write: The area of triangle as an algebraic expression and evaluate it at the given value..

Answer to Problem 36PPS

The algebraic expression for area is $\frac{h^2}{2}+3h$ and when $h=12inches$ , area is $A=108inche{s}^2$ .

Explanation of Solution

Given information:

The right angled triangle is given with height $h$ and base $h+6$ is given. Also, then $h=12inches$ is given.

Concept and Formula Used:

We use the formula for area of triangle given by

  $\frac{1}{2}\times base\times height$

Calculation:

As the given right angled triangle has height $h$ and base $h+6$ , so the area of triangle is

  $\begin{array}{l}A=\frac{1}{2}\times h\times \left(h+6\right)\\ A=\frac{1}{2}\left(h^2+6h\right)\\ A=\frac{h^2}{2}+3h\end{array}$

Now, if $h=12inches$ , the area is

  $\begin{array}{l}A=\frac{{\left(12\right)}^2}{2}+3\left(12\right)\\ A=\frac{12\times 12}{2}+36\\ A=6\times 12+36\\ A=72+36\\ A=108inche{s}^2\end{array}$

Conclusion:

The algebraic expression for area is $\frac{h^2}{2}+3h$ and when $h=12inches$ , area is $A=108inche{s}^2$ .