The area of a parallelogram PQRS is `36 cm^(2)`. M is any point on the side RS. The area of `Delta PMQ` is.

Options

A. `18 cm^(2)`
B. `9 cm^(2)`
C. `36 cm^(2)`
D. `12 cm^(2)`

Answer

To find the area of triangle PMQ given that the area of parallelogram PQRS is 36 cm², we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The area of parallelogram PQRS is given as 36 cm².
- M is any point on the side RS of the parallelogram.

2. **Identify the Relationship**:
- The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]
- For parallelogram PQRS, we can take PQ as the base and PM as the height.

3. **Set Up the Equation**:
- Let the length of base PQ be \( b \) and the height PM be \( h \).
- From the area of the parallelogram, we have:
\[ b \times h = 36 \text{ cm}^2 \]

4. **Calculate the Area of Triangle PMQ**:
- The area of triangle PMQ can be calculated using the formula:
\[ \text{Area of } \Delta PMQ = \frac{1}{2} \times \text{Base} \times \text{Height} \]
- Here, the base is PQ (which is \( b \)) and the height is PM (which is \( h \)).
- Substituting the values, we get:
\[ \text{Area of } \Delta PMQ = \frac{1}{2} \times b \times h \]

5. **Substitute the Area of the Parallelogram**:
- Since we know that \( b \times h = 36 \text{ cm}^2 \), we can substitute this into the triangle area formula:
\[ \text{Area of } \Delta PMQ = \frac{1}{2} \times 36 \text{ cm}^2 = 18 \text{ cm}^2 \]

6. **Final Answer**:
- Therefore, the area of triangle PMQ is:
\[ \text{Area of } \Delta PMQ = 18 \text{ cm}^2 \]