Question

if in the given figure, abcd is a parallelogram. if area of triangle BAP=10 cm square and area of triangle CPD=30 cm square, then area of parallelogram ABCD is ?

Answer 1

The area of parallelogram ABCD is 80 cm².

Step-by-step explanation:

It is given that,

ABCD is a parallelogram

Area of triangle BAP = 10 cm²

Area of triangle CPD = 30 cm²

Step 1:

We know that if a triangle and a parallelogram are on the same base and lie between the same parallel lines, then the area of the triangle is equal to half the area of the parallelogram.

Here we have ∆ PBC and parallelogram ABCD have the same base BC and lie between the same parallel lines BC and AD.  

∴ Area (∆ PBC) = ½ * Area (parallelogram ABCD)  

⇒ Area (parallelogram ABCD) = 2 * Area (∆ PBC) ……. (i)

Step 2:

From the given figure, we can write  as,

Area( parallelogram ABCD ) = Area( ∆ CPD ) + Area( ∆ BAP ) + Area( ∆ PBC )

⇒ 2 * Area (∆ PBC) = Area(∆ CPD ) + Area(∆ BAP ) + Area(∆ PBC ) …… [substituting from (i)]

⇒ 2 * Area (∆ PBC) - Area( ∆ PBC ) = Area( ∆ CPD ) + Area( ∆ BAP )

⇒ Area (∆ PBC) = Area( ∆ CPD ) + Area( ∆ BAP )

Substituting the given values of ∆ CPD & ∆ BAP

⇒ Area (∆ PBC) = 30 + 10

⇒ Area (∆ PBC) = 40 cm² …… (ii)

Step 3:

Thus, substituting eq. (ii) in (i), we get

The area of parallelogram ABCD,

= 2 * 40

= 80 cm²

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Also View:

Theorem 9.1 parallelogram on the same base and between the same parallels are equal in area.  

https://brainly.in/question/6334507

Prove that parallelograms on the same base and between the some parallels are equal is area.

https://brainly.in/question/8936215

Answer 2

Step-by-step explanation:

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