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## 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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