Chapter 9.7, Problem 15PSB

To determine

To calculate: The perimeter of the isosceles trapezoid EFGH.

Answer to Problem 15PSB

The perimeter of the isosceles trapezoid is 38 units

Explanation of Solution

Given information :

A trapezoid with measures of parallel sides as 10 units and 16 units

One base angle is 60 $°$

Formula used :

In $30°-60°-90°$ triangle ratio of sides is $1:\sqrt{3}:2$

Perimeter of figure is sum of its sides.

Calculation :

In isosceles trapezoid EF = HG

EH = 10 and FG = 16......given

  $\angle \text{EFG}=60°$ ......given

  

Draw perpendiculars from points E and H so as it cuts FG at X and Y

Now, FX = YG = 3 units and XY = 10

In triangle EXF we have

  $\angle \text{EFX}=60°$ and $\angle \text{EXF}=90°$

Therefore, triangle EXF is $30°-60°-90°$

Thus, sides of this triangle will be in the ratio $1:\sqrt{3}:2$

  $\therefore$ FX = x (say) =3 units $\Rightarrow$ EF = 2x = 6 units

  $\therefore$ Required perimeter = EF + FG + GH + HE = 6 +16 + 6 +10 = 38 units