Question

"Question 5 In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) ar (PQRS) = ar (ABRS) (ii) ar (AXS) = ar (PQRS)

Class 9 - Math - Areas of Parallelograms and Triangles Page 159"

Answer 1

Parallelograms on the same base and between the same parallels are equal in area.

If a parallelogram and a triangle are on the same base and between the same parallels then area of the triangle is half the area of the parallelogram.

 

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Given:

PQRS & ABRS both are parallelograms and X is any point on BR.

To show:

(i) ar (PQRS) = ar (ABRS)

(ii) ar (AXS) = ar (PQRS)

Proof:

 

(i)  Here, Parallelograms PQRS and ABRS lie on the same base SR and between the same parallel lines SR and PB.

∴ ar(PQRS) = ar(ABRS) — (i)

(ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and between the same parallel lines AS and BR.

∴ ar(ΔAXS) = 1/2 ar(ABRS) — (ii)

From eq (i) and (ii),

ar(ΔAXS) = 1/2 ar(PQRS)

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Hope this will help you...

 

Answer 2

here is your answer....