Question

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

Answer 1

`Area = 52\sqrt3 \ ft^2`

Explanation:

Area of trapezoid

`((a+ b)/(2)) * h` -----------( 1 )

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

`sin 60 = (opposite)/(hypotenuse)`
`[ opposite \ in \ the \ equation \ \ is \ the \ height \ of \ the \ trapezoid ]`

`(\sqrt3)/(2) = (opposite )/( 8)\\\\(\sqrt3)/(2) * 8 = opposite\\\\4\sqrt3 = opposite`

Therefore, h = 4√3 ft

`cos 60 = (adjacent)/(hypotenuse)`
`adjacent \ in \ the\ equation \ is \ the\ base \ of \ the \ triangle ]`

`(1)/(2) = (adjacent)/(hypotenuse)\\\\(1)/(2) * 8 = adjacent\\\\4 = adjacent`

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

Substitute the values in the Area equation :

`Area = (11 + 15)/(2) * 4 \sqrt3 = (26)/(2) * 4\sqrt3 = 13 * 4\sqrt3=52\sqrt3 \ ft^2`