A trapezoid with congruent base angles have the other two sides (that are not the bases) congruent to each other:
And the area A of a trapezoid with bases a and b, and height h is given by:
[tex]A=\frac{a+b}{2}\cdot h[/tex]Thus, we need to find the height h of this trapezoid and then use it to calculate its area.
Step 1
We can find h by using the tangent of 45º. We obtain:
[tex]\begin{gathered} \frac{h}{6}=\tan 45^{\circ} \\ \\ \frac{h}{6}=1 \\ \\ h=1\cdot6 \\ \\ h=6 \end{gathered}[/tex]Step 2
Now, we have:
a = 24
b = 36
h = 6
Thus, the area A of the trapezoid is:
[tex]\begin{gathered} A=\frac{24+36}{2}\cdot6 \\ \\ A=\frac{60}{2}\cdot6 \\ \\ A=30\cdot6 \\ \\ A=180 \end{gathered}[/tex]
