Chapter 11.1, Problem 30PPS

To determine

To calculate: The area of the given triangle.

Answer to Problem 30PPS

The area of the given triangle is $A=194.3c{m}^2$ .

Explanation of Solution

Given information: The triangle is given below.

  

Formula used:

The area of a triangle is given by

  $\begin{array}{l}A=\frac{1}{2}\times \left(b\times h\right)\\ b\text{is}\text{the}\text{base}\text{of}\text{the}\text{triangle}\text{.}\\ h\text{is}\text{the}\text{height}\text{.}\end{array}$

Calculation:

From the given information it can be observed that

  $\begin{array}{c}h=12cm\&b=b_1+b_2\\ \text{Where,}\tan {29}^{\circ }=\frac{12}{b_1}\\ b_1=\frac{12}{\left(\tan {29}^{\circ }\right)}\\ b_1=\frac{12}{\left(0.55\right)}=21.81cm\\ \\ \text{And,}{\left(12\right)}^2+{\left(b_2\right)}^2={\left(16\right)}^2\\ b_2=\sqrt{\left(256-144\right)}=10.58cm\end{array}$

So $b=b_1+b_2=21.81+10.58=32.39cm$

The area of the given triangle is

  $\begin{array}{c}A=\frac{1}{2}\times \left(b\times h\right)\\ =\frac{1}{2}\times \left(32.39\times 12\right)\\ A=194.34c{m}^2\\ A=194.3c{m}^2\end{array}$

Therefore the area of the given triangle is $A=194.3c{m}^2$ .