MCQ
Write the correct answer of the following: If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is:
- A$1 : 3$
- ✓$1 : 2$
- C$3 : 1$
- D$1 : 4$
✓
Answer
Correct option: B.
$1 : 2$
We know that, if a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.
i.e., $\text{Area of triangle}=\frac{1}{2}\ \text{Area of parallelogram}$
$\Rightarrow\frac{\text{Area of triangle }}{\text{Area of parallelogram}}=\frac{1}{2}$
$\therefore$ Area of triangle : Area of parallelogram = $1 : 2$
i.e., $\text{Area of triangle}=\frac{1}{2}\ \text{Area of parallelogram}$
$\Rightarrow\frac{\text{Area of triangle }}{\text{Area of parallelogram}}=\frac{1}{2}$
$\therefore$ Area of triangle : Area of parallelogram = $1 : 2$
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