Chapter 11.1, Problem 31PPS

To determine

To calculate: The area of the given triangle.

Answer to Problem 31PPS

The area of the given triangle is $A=187.7m{m}^2$ .

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

  $\begin{array}{c}b=23mm\\ \\ \text{And,}\sin {51}^{\circ }=\frac{h}{21}\\ h=21\left(\sin {51}^{\circ }\right)\\ h=21\left(0.77\right)=16.32mm\end{array}$

The area of the given triangle is

  $\begin{array}{c}A=\frac{1}{2}\times \left(b\times h\right)\\ =\frac{1}{2}\times \left(23\times 16.32\right)\\ A=187.68m{m}^2\\ A=187.7m{m}^2\end{array}$

Therefore the area of the given triangle is $A=187.7m{m}^2$ .