Question

Find the area of the trapezoid. Leave your answer in simplest radical form.

Answer 1

Answer:

$Area = 52\sqrt3 \ ft^2$

Step-by-step explanation:

Area of trapezoid

                         $(\frac{a+ b}{2}) \times h$      -----------( 1 )

We will split the trapezoid into Triangle and rectangle. To find the height and full length of base.

$sin 60 = \frac{opposite}{hypotenuse}$   $[ opposite \ in \ the \ equation \ \ is \ the \ height \ of \ the \ trapezoid ]$

$\frac{\sqrt3}{2} = \frac{opposite }{ 8}\\\\\frac{\sqrt3}{2} \times 8 = opposite\\\\4\sqrt3 = opposite$

Therefore, h = 4√3 ft

$cos 60 = \frac{adjacent}{hypotenuse}$    $adjacent \ in \ the\ equation \ is \ the\ base \ of \ the \ triangle ]$

$\frac{1}{2} = \frac{adjacent}{hypotenuse}\\\\\frac{1}{2} \times 8 = adjacent\\\\4 = adjacent$

Therefore, a = 11 feet, b = 11 + 4 = 15 feet

Substitute the values in the Area equation :

                                                $Area = \frac{11 + 15}{2} \times 4 \sqrt3 = \frac{26}{2} \times 4\sqrt3 = 13 \times 4\sqrt3=52\sqrt3 \ ft^2$