# 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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.`

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