Question
A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is:
- 1 : 1
- 1 : 2
- 2 : 1
- 1 : 3
✓
Answer
- 1 : 2
Area of a triangle DFC $=\frac{1}{2}\times\text{base}\times\text{height}\\=\frac{1}{2}\times\text{DC}\times\text{FG}=\frac{1}{2}\times\text{DC}\times\text{h}$
Area of parallelogram ABCD = base × height = DC × AE = DC × h
Required Ratio $=\frac{\frac{1}{2}\times\text{DC}\times\text{h}}{\text{DC}\times\text{h}}=1:2$
Hence, correct option is (b).
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