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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