Question

a parallelogram ADCE is drawn in a Trapezium ABCD as shown in figure the area of the parallelogram is 96 CM square find the area of the trapezium. ​

Answer 1

Answer:

area of trapezium is 144 CM square

Answer 2

The area of ABCD=144 square cm

Step-by-step explanation:

ADCE is a parallelogram

We know that diagonal of parallelogram divides the parallelogram in to two triangle of equal area.

Ar(ABE)=Ar(ECD)

Ar(ADCE)=96 square cm

Ar(ABE)+ar(ECD)=Ar(ADCE)

Ar(ABE)+ar(ABE)=96

$2Ar(ABE)=96$

$Ar(ABE)=\frac{96}{2}=48cm^2$

$Ar(ABE)=Ar(ECD)=48cm^2$

EC is a transversal line and ED is parallel o  

Angle ECD=angle CEB

Angle ECB=Angle CED

Reason: Alternate interior angle are equal

Angle ECD+angle ECB=Angle CEB+angle CED

Angle DCB=Angle DEB

When opposite angles are equal then the quadrilateral is a parallelogram.

Therefore, quadrilateral EBCD is a parallelogram.

Ar(EBC)=Ar(DCE)

Ar(EBC)=48 square cm

Ar(ADCE)+AR(CEB)=96+48=144 square cm

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