Answer:
20 sq.units
Step-by-step explanation:
Given: The base of a parallelogram is 8 units, and the height is 5 units. A segment divides the parallelogram into two identical trapezoids. The height of each trapezoid is 5 units
To Find: Area of one of the trapezoid.
Solution: Consider the file attached with solution.
In Parallelogram ABCD,
[tex]\text{CD}[/tex]=[tex]8\text{unit}[/tex]
[tex]\text{height}=5\text{unit}[/tex]
therefore,
area of parallelogram [tex]area(\text{ABCD})=\text{base}\times\text{height}[/tex]
[tex]8\times5[/tex]
[tex]area(\text{ABCD})[/tex]=[tex]40\text{unit}[/tex]
Segment EF divides parallelogram in two identical trapezoid AEFD and CFEB
therefore,
[tex]area(\text{AEFD})=area(\text{CFEB})[/tex]
also,
[tex]area(\text{AEFD})+area(\text{CFEB})=area(\text{ABCD})[/tex]
now area of one of the trapezoid [tex]\text{AEFD}[/tex]
[tex]2\times area(\text{AEFD})=area(\text{ABCD})[/tex]
[tex]area(\text{AEFD})=\frac{area(\text{ABCD})}{2}[/tex]
[tex]area(\text{AEFD})=\frac{40}{2}=20[/tex]
The area of trapezoid is [tex]20\text{sq.units}[/tex]
