Chapter 9.7, Problem 19PSB

To determine

To calculate:The Perimeter of trapezoid to the nearest tenth.

Answer to Problem 19PSB

Perimeter of trapezoid is $57.9$ units.

Explanation of Solution

Given information:

Here, we have given one trapezoid.

Formula used: Perimeter of rhombus = $4$ (side)

Calculation: Let ABCD be the trapezoid. Draw a perpendicular BP to CD such that BP = $8$ and DP = $10$ .

Now, as the angles of triangle BPD are $30°,60°,90°$ ,

Perpendicular = $8$

  $\Rightarrow BC=2(8)=16$ and $CP=8\sqrt{3}$ (If one side of right triangle is $a$ , then hypotenuse is $2a$ and remaining side is $a\sqrt{3}$ ).

Now, Perimeter of trapezoid = Sum of all sides

  $\begin{array}{l}\Rightarrow AB+BC+CP+PD+DA\\ \Rightarrow 10+16+8\sqrt{3}+10+8\\ \Rightarrow 44+8\sqrt{3}\\ \Rightarrow 44+13.85\\ \Rightarrow 57.85\end{array}$

Nearest tenth = $57.9$ units