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∆ABC is an equilateral triangle and D and E are midpoints of AB and BC respectively. Then the area of ∆ABC : the area of the trapezium ADEC is
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- 5 : 3
- 4 : 1
- 8 : 5
- 4 : 3
- 5 : 3
Correct Option: D
Let, AB = BC = CA = 2x units
∴ BD = BE = x units
| Area of ∆ABC = | × (2x)² | |
| 4 |
= √x² sq. units
| Area of ∆BDE = | x² | |
| 4 |
| ∴ Area of a trapezium ADEC = |  | √3x² - | x² |  | sq. units | |
| 4 |
| = | sq. unit | |
| 4 |
| ∴ Required ratio = √3x² : | x² = 4 : 3 | |
| 4 |
