Question

The area of a
parallelogram field PQRS
is 56 square units. The
diagonals PR and QS
intersect each other at
point O. Find the area of the shaded region.​

Answer 1

First of all, we would try to prove that the triangles SOP, SOR, ROQ and POQ are congruent to each other.

So, In ∆SOP and ∆SOR

Angle(PSO) = Angle(OSR)

OS = OS .......(common side)

and, PO = OR.

Thus, by SAS congruency rule,

∆SOP is congruent to ∆SOR

Similarly, we can prove that all other triangles are congruent to each other.

Now, Since all the triangles are congruent to each other, thus, their areas must be equal.

So,

Ar(SOP) = Ar(SOR) = Ar(ROQ) = Ar(POQ) = 1/4[Ar(PORS)]. ..............(1)

Therefore, from Equation (1) we can conclude that Area of Shaded figure is 3/4 the area of parallelogram PQRS.

=> Area of shaded figure = 3(56)/4

= 14 × 3

= 42 square units.

Thus, the correct answer is 42 square units.

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