To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]
where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]
Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]
Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]
Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]
Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]
