Question

Does anyone know how to do this ?

Answer 1

Answer: D) 32

Explanation:

The area of a parallelogram equals its base times its height. Substitute the base and area into this formula to solve for the height:

A=bh

40=(5)(h)

h=8

If ABCD is a parallelogram, opposite sides are parallel, so AB is parallel to DC. If AB is parallel to DC, EB is parallel to DC. Since EB is parallel to DC, quadrilateral EBCD has at least one pair of parallel sides, making it a trapezoid. The area of a trapezoid is equal to
`(h(b_(1)+b_(2)) )/(2)` where h is the height,
`b_(1)` is one base, and
`b_(2)` is the other base. Plug the necessary values into the formula:

A=
`(h(b_(1)+b_(2)) )/(2)`

`b_(1) =AB-AE\\DC=AB\\b_(1) =DC-AE\\b_(1) =5-2\\b_(1) =3`

`b_(2) =5`

h=8

A=
`(8(3+5))/(2)`

A=32

The answer is D) 32.