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The problem provided is in Hindi and seems to be based on the concept of geometry, specifically related to quadrilaterals. Here's a breakdown of the problem:

**Translation and Explanation**:
- The given quadrilateral is **PQRS**, and it is a general quadrilateral where \(PR\) is a diagonal.
- \(PR = 144\) cm.
- There is a perpendicular line from point \(Q\) to \(PR\) at point \(M\), such that \(QM \perp PR\) and \(QM = 22\) cm.
- Another perpendicular line \(SL \perp PR\), with \(SL = 28.5\) cm.
- We are asked to find the **area** of quadrilateral **PQRS**.

### Approach:
The area of quadrilateral **PQRS** can be computed by dividing it into two triangles: \( \triangle PQR \) and \( \triangle PRS \), using diagonal \(PR\). Then, the total area will be the sum of the areas of these two triangles.

1. **Area of triangle \(PQR\)**:
   - This triangle has base \(PR\) and height \(QM\), which is given.
   - Area of \( \triangle PQR = \frac{1}{2} \times PR \times QM\)

2. **Area of triangle \(PRS\)**:
   - This triangle also has the same base \(PR\) and height \(SL\).
   - Area of \( \triangle PRS = \frac{1}{2} \times PR \times SL\)

Finally, adding both areas will give the area of quadrilateral PQRS.

Let's calculate it:

\[
\text{Area of } PQRS = \frac{1}{2} \times PR \times QM + \frac{1}{2} \times PR \times SL
\]

\[
= \frac{1}{2} \times 144 \times 22 + \frac{1}{2} \times 144 \times 28.5
\]

Let me compute the result.The total area of quadrilateral **PQRS** is **3636 cm²**.

Would you like more details on how this solution was derived or have any other questions?

Here are five related questions for further practice:
1. How would the area change if the length of \(QM\) was 30 cm?
2. Can you calculate the area of a quadrilateral if both perpendiculars were the same length?
3. What formula would you use if the diagonal was not perpendicular to the sides?
4. How can you determine the height if only the area and base of the triangle are known?
5. What would be the area of the quadrilateral if \(PR\) was shorter?

**Tip**: Always break complex quadrilaterals into triangles when calculating their area; this simplifies the process.

दिए गए चतुर्भुज PQRS में, PR = 144 सेमी, QM ⊥ PR, SL ⊥ PR, QM = 22 सेमी, SL = 28.5 सेमी है। PQRS चतुर्भुज का क्षेत्रफल ज्ञात करें।

Solve for the area of quadrilateral PQRS using the given dimensions: PR = 144 cm, QM = 22 cm, and SL = 28.5 cm. Learn the step-by-step breakdown of the geometry problem, applying basic area formulas for triangles.

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