In the figure,ABCD is a parallelogram and BE is a line segment.If DE=2AD,and the area of ABCD is 20cm^2,find the area of triangle ABE.This is the figure http://bit.ly/AjpK8F

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to remember the area of parallelogram is double the area of triangle ABD (look at the figure).

Use the following formula to calculate the area of triangle ABD:

`A_(ABD) = (AB*AD*sin(BAD))/2`

Hence, the area of parallelogram is `2A_(ABD).`

`A_(ABCD) = 2A_(ABD)`

Plugging the value of area of parallelogram in the formula above yields:

`20 = 2*(AB*AD*sin(BAD))/2 =gt (AB*AD*sin(BAD)) = 20`

Evaluating the area of triangle ABE yields:

`A_(ABE) = (AE*AB*sin(EAD))/2`

Using the fact that angles EAD and BAD have equal measures and AE = 2AD yields:

Evaluating the area of triangle ABE yields:

`A_(ABE) = (2AD*AB*sin(BAD))/2`

Reducing like terms yields:

`A_(ABE) = (AD*AB*sin(BAD))`

`` Notice that `A_(ABE) = A_(ABCD).`

Hence, evaluating the area of triangle ABE yields: `A_(ABE) = A_(ABCD) = 20 cm^2.`

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question