Question

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

Answer 1

Answer:

= 32√3 ft²

Step-by-step explanation:

Area of the trapezoid will be equal to the area of the square and that of the triangle.

Considering the triangle part;

Cos 60 = x/8

x = 8 × sin  60

   = 4

Base of the triangle part = 4 ft

Therefore, top of the trapezoid = 6 ft

Height = 8 × sin 60

            = 8 × √3/2

           = 4 √3

Area of the trapezoid

Area = ((a+b)/2) × h

        = ((6 + 10 )/2 )× 4√3

        = 16/2 × 4√3

        = 32√3 ft²

           

 

Answer 2

Answer:

4th option is correct

Step-by-step explanation:

Here in the triangle we have angle = 60

hypotenuse= 8

opposite and adjacent can be solved using trigonometric ratios

cos 60  = $\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}$

which gives adjacent = 4  on solving

likewise using sine we can find opposite side to the angle which is height of

trapezium.

sin60$\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}$

therefore height =$4\sqrt{3}$ and adjacent = 4  ft

therefore opposite sides of Trapezium are 10 ft and 6 ft  

Formula for area of Trapezium =$\frac{1}{2}$(sum of parallel sides)x height

=      $\frac{1}{2}$(10+6)x $4\sqrt{3}$

on solving it ,we get  $32\sqrt{3}$