Chapter 12.3, Problem 57SR

To determine

To find : Theperimeter and area of the composite figure.

Answer to Problem 57SR

Perimeter and area of the composite figure are 180 in. and $1887$ in.²respectively.

Explanation of Solution

Given information :

A parallelogram ACDE whose base is 39 in. and height is 37 in. And, there is a triangle ABC whose base is 37 in. and height is 24 in.

Formula used : Using the area of parallelogram = $b\times h$ , where AE will be the $b$ and AB will the $h$ we can find the area.And for the area of the triangle, Area = $\frac{1}{2}(AB\times BC)$ , where AB will be base and BC will be height. To find perimeter we will have to find the hypotenuse of $△ABC$ . So, we will use the Pythagoras theorem, $AC=\sqrt{A{B}^2+B{C}^2}$ . To find the perimeter we will add all sides of the composite fig.

Calculation : Calculate the area of composite fig.

Area of the composite figure will be $AreaofparallelogramACDE+AreaoftriangleABC$

$=\left(AE\times AB\right)+\frac{1}{2}(AB\times BC)$

$=\left(39\times 37\right)+\frac{1}{2}\left(37\times 24\right)$

$=1443+444$

$=1887$ in.2

Now, calculate the perimeter of composite figure.

To calculate the perimeter, we have to find the hypotenuse of triangle ABC.

AC $=\sqrt{A{B}^2+B{C}^2}$

$=\sqrt{{37}^2+{24}^2}$

$=\sqrt{1945}$

$=44.1$ in.

We know, perimeter $=Sumofallsides$

  $=AB+BC+CD+DE+AE$

$=37+24+39+44.1+39$

  $\text{=183}\text{.1}$ in.

$=180$ in.