Question

25. If 3, 5 be the distances between the parallel sides and 30° is the angle between two adjacent sides of
a parallelogram then its area
1) 15/2
2) 15
3) 30
4) 15/4​

Answer 1

Answer:

The area of the parallelogram is 1)15/2.

Step-by-step explanation:

Let ABCD be the parallelogram whose area is to be calculated.

It is given that the distances between the parallel sides is 3 and 5. Therefore, AB = CD = 3 and AD = BC = 5.

The angle between the adjacent sides is given to be 30°. Hence, ∠B = 30°.

We know that the area of parallelogram is given as follows:

A(parallelogram) = Base × Height

A(parallelogram) = Base × Adjacent side × sinθ

In case of parallelogram ABCD, the base is BC, adjacent side is AB, and θ=30°. Therefore,

A(parallelogram) = BC × AB × sinθ

Substituting the given values, we get

A(parallelogram) = 5×3×sin30°

A(parallelogram) = 15×(1/2)

A(parallelogram) = 15/2

Therefore, the area of the given parallelogram is 15/2.

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