Question

What is the area of this trapezoid (the right leg says 8 btw)

Answer 1

The answers have square roots among the choices so we probably shouldn't use that calculator button.

We can't just apply the area of the trapezoid formula

$A = \frac 1 2(b + t) h$

where b is the bottom base, t the parallel top, and h the height, because we don't know the top t.

It will be 10 less the leg of that right triangle, which we calculate as

$l = \sqrt{8^2 - (4\sqrt{3})^2} = \sqrt{64 - 48} = \sqrt{16}=4$

Now we can apply the trapezoid formula. We have

$b = 10, \qquad t=10-4=6, \qquad h= 4\sqrt{3}$

$A = \frac 1 2(b + t) h = \frac 1 2 (10 +6)(4 \sqrt{3}) = 32 \sqrt{3}$

Choice b