Answer: second option
Step-by-step explanation:
Find the distance AE by subtracting AB and DC and dividing by 2:
[tex]AE=\frac{AB-DC}{2}\\\\AE=\frac{15ft-7ft}{2}\\\\AE=4ft[/tex]
Knowing the length of AD and AE, you can apply the Pythagorean Theorem to calculate the length DE:
[tex]c=\sqrt{a^2-b^2}[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
Then:
[tex]a=AD=5ft\\b=AE=4ft\\c=DE[/tex]
Substituting values into [tex]c=\sqrt{a^2-b^2}[/tex] you get that the lenght of DE is:
[tex]DE=\sqrt{(5ft)^2+(4ft)^2}\\DE=3ft[/tex]
Calculate thea area of the trapezoid with the formula:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where h is the height, B is the larger base and b is the smaller base.
Substituting, you get:
[tex]h=DE=3ft\\B=AB=15ft\\b=DC=7ft\\\\A=\frac{3ft}{2}(15ft+7ft)=33ft^2[/tex]
