Chapter 58, Problem 1A

Find the area of this figure. Round your answer to 2 decimal places.

To determine

Area of given figure round to 2 decimal places.

Answer to Problem 1A

Area of given figure is $11.62\text{in}{\text{.}}^2$.

Explanation of Solution

Given:

  

  $l_1=0.418\text{in}\text{.}$

  $b_1=3\text{in}\text{.}$

  $l_2=15\text{in}\text{.}$

  $b_2=0.524\text{in}\text{.}$

  $b_3=0.416\text{in}\text{.}$

  $h=3\text{in}\text{.}$

The shaded diagram is represented as:

  

The above diagram is divided into three parts.

The area of diagram can be calculated as:

  $A=2A_1+A_2+2A_3$ ... Eq. (1)

Now

  $A_1=l_1{b}_1$

  $A_1=\left(0.418\times 3\right)\text{in}{\text{.}}^2$

  $A_1=1.254\text{in}{\text{.}}^2$

Then

  $A_2=l_2{b}_2$

  $A_2=\left(15\times 0.524\right)\text{in}{\text{.}}^2$

  $A_2=7.86\text{in}{\text{.}}^2$

Then

  $A_3=\frac{1}{2}{b}_{3}h$

  $A_3=\frac{1}{2}\left(0.416\text{in}\text{.}\right)\left(\text{3}\text{in}\text{.}\right)$

  $A_3=0.624\text{in}{\text{.}}^2$

Substitute the values of $A_1$, $A_2$ and $A_3$ in Eq. (1)

  $A=2A_1+A_2+2A_3$

  $A=2\left(1.254\text{in}{\text{.}}^2\right)+\left(7.86\text{in}{\text{.}}^2\right)+2\left(0.624\text{in}{\text{.}}^2\right)$

  $A=11.62\text{in}{\text{.}}^2$

Therefore, the area of given figure is $11.62\text{in}{\text{.}}^2$.