Question

3. Find the area of the trapezoid.
8 ft
4V3
10 ft

Answer 1

`32\sqrt3`

Explanation:

We need first to find the measure of the red horizontal line, call it x. The triangle i filled is a right triangle, so we can apply pythagoras theorem,

`8^2 = x^2+(4\sqrt3)^2 \rightarrow 64=x^2+(16*3) \\x^2=64-48 \rightarrow x^2=16 \rightarrow x=4`

(we are talking lengths of segment so we take only the positive root!)

At this point we can find the length of the smaller base of the trapezoid (which is
`10-4=6`) and apply the formula, or split the figure in a rectangle of sides 6 and
`4\sqrt3` and a triangle of sides
`4\sqrt3` and 4.

With the trapezoid formula

`A=\frac12(B+b)h = \frac12(10+6)4\sqrt3 = 32\sqrt3`

With the sum of figures:

`A= bh+\frac12 xh=6*4\sqrt3 +\frac12*4*4\sqrt3=24\sqrt3+8\sqrt3=32\sqrt3`