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

Question

janu16 · Answer

Here is the pic

janu16 · Answer

Help plz

anonymous · Answer

use sine and cosine to find the dimensions of the triangle.. then you can find the area of the triangle and the rectangle and add them together.

janu16 · Answer

But how do you use sine and cosine? You use it for triangle?

anonymous · Answer

what mathematics class is this for?

janu16 · Answer

Geometry

anonymous · Answer

have you learnt the unit circle?

janu16 · Answer

Ya it has been a long time

anonymous · Answer

You would use the functions sine and cosine with 60 degrees to find the rest of the dimensions.

janu16 · Answer

You mean press sin than (8)60

phi · Answer

perhaps you learned about 30-60-90 triangles?
the side opposite the 30 degree angle (i.e. the "short" leg) is 1/2 the hypotenuse
and the other leg opposite the 60 degree angles is sqr(3) * h/2  (where h is the hypotenuse=8 in your problem)

janu16 · Answer

But how do you put that in calculator

janu16 · Answer

@phi

phi · Answer

they say " leave your answer in simplest radical form"
so they don't expect you to use a calculator.
the height of the triangle is  $$\frac{8 \sqrt{3}}{2} = 4 \sqrt{3} $$

janu16 · Answer

Ok and don't you find area of rectangle?

janu16 · Answer

@phi

phi · Answer

you could find the area of the rectangle and of the small triangle and add them up
or you could find the area of the trapezoid
= (top+bottom)/2 * height

to finish this problem, you need to find the "short leg" of the 30-60-90 triangle.
it is hypotenuse/2