Answer:
Area = 170 ft^2
Step-by-step explanation:
Area of Trapezoid is given by the formula [tex]A=\frac{1}{2}(b_1+b_2)h[/tex]
Where
b1 and b2 are the two bases (parallel sides)
h is the height
In our diagram, the two bases are 12 and 22, but the height (let it be h) isn't given. To find the height (the dotted line), we use the right triangle which has an angle given as 45°.
Since the height is the "opposite" side to angle and we know the base of the triangle (22-12=10), which is the "adjacent" side, we can use the ratio of tan. Note, tan 45° = 1.
[tex]Tan(45)=\frac{h}{10}\\h=Tan(45)*10\\h=1*10\\h=10[/tex]
Now we can plug the information into the formula and solve for area. So:
Area = [tex]A=\frac{1}{2}(b_1+b_2)h\\A=\frac{1}{2}(12+22)(10)\\A=\frac{1}{2}(34)(10)\\A=170[/tex]
Thus Area = 170 ft^2
