Question

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. Draw the parallelogram and the two trapezoids on the grid shown. Then find the area of one of the trapezoids. *The grid is a normal grid*

Answer 1

so it is a line of symmetry. 8x5=40 so the area of one is 40.

Answer 2

20 sq.units

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,

`\text{CD}`=
`8\text{unit}`

`\text{height}=5\text{unit}`

therefore,

area of parallelogram
`area(\text{ABCD})=\text{base}*\text{height}`

`8*5`

`area(\text{ABCD})`=
`40\text{unit}`

Segment EF divides parallelogram in two identical trapezoid AEFD and CFEB

therefore,

`area(\text{AEFD})=area(\text{CFEB})`

also,

`area(\text{AEFD})+area(\text{CFEB})=area(\text{ABCD})`

now area of one of the trapezoid
`\text{AEFD}`

`2* area(\text{AEFD})=area(\text{ABCD})`

`area(\text{AEFD})=\frac{area(\text{ABCD})}{2}`

`area(\text{AEFD})=(40)/(2)=20`

The area of trapezoid is
`20\text{sq.units}`