Chapter 7.1, Problem 46HP

To determine

Calculate the percent of triangle which is not shaded.

  

Answer to Problem 46HP

Percent of triangle which is not shaded is 88.8%

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate whole area of triangle,

  $\begin{array}{l}Areaoftriangle=\frac{1}{2}(Base\times Height)\\ =\frac{1}{2}(12\times 9)\\ =\frac{108}{2}\\ =54i{n}^2\end{array}$

Area of shaded triangle,

  $\begin{array}{l}Areaofshadedtriangle=\frac{1}{2}(Base\times Height)\\ =\frac{1}{2}(4\times 3)\\ =\frac{12}{2}\\ =6i{n}^2\end{array}$

  $\begin{array}{l}\begin{array}{l} \hfill \\ \left[Areaoftrianglewhichisnotshaded\right]=\left[Wholeareaoftriangle\right]-\left[Areaofshadedtriangle\right]\hfill \end{array}\\ =\left[54-6\right]i{n}^2\\ =48i{n}^2\end{array}$

Now we have to calculate percent of area of triangle which is not shaded,

  $\begin{array}{l}\begin{array}{l} \hfill \\ \left[PercentofAreaoftrianglewhichisnotshaded\right]=\frac{Areaoftrianglewhichisnotshaded}{Wholeareaoftriangle}\hfill \end{array}\\ =\frac{48}{54}\\ =0.888\\ =0.888\times 100\\ =88.8\%\end{array}$

Conclusion:

Therefore, we are able to calculate percent of area of triangle which is not shaded.