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In the figure above, the area of the parallelogram is – OGQR 2020 Question #85 with Solution

OGQR 2020: Question No. 85

In the figure above, the area of the parallelogram is

Source OGQR 2020
Type Problem Solving
Topic Geometry
Sub-Topic Quadrilateral
Difficulty Medium

Solution

Given

In this question, we are given

  • The diagram of a parallelogram, where the adjacent sides are of length 8 and 12
  • One angle between the sides is 60°

To Find

We need to determine

  • The area of the parallelogram

Approach & Working

Let us assume the parallelogram is PQRS, and QT is the perpendicular dropped from point Q to the side PS.

  • Hence, we can say that PQT is a 30°-60°-90° triangle, and the side ratio is 1: √3: 2.
  • QT: PQ = √3: 2

Or, QT = √3/ 2 * PQ = √3/ 2 * 8 = 4√3

  • Therefore, the area of the quadrilateral = PS * QT = 12 * 4√3 = 48√3 (PS = QR)

Hence, the correct answer is option D.

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