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The problem is stated as follows:

In triangle \( PQR \), point \( K \) is selected on side \( PQ \), and point \( L \) is selected on side \( QR \). The segments \( PL \) and \( KR \) intersect at point \( T \). We need to find the area of triangle \( PQR \) given the following areas:
- \( S_{PKT} = 9 \)
- \( S_{PDR} = 10 \)
- \( S_{RTL} = 11 \)

Let’s solve this problem step-by-step by utilizing the properties of area ratios and similar triangles that may be formed by intersecting lines inside a triangle.

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### Related Questions
1. How can we find the area of a triangle when segments intersect inside it?
2. What is the significance of areas of sub-triangles formed by intersecting lines?
3. How can area ratios help in solving problems related to intersecting triangles?
4. What are some common strategies for solving geometry problems with intersecting triangles?
5. How can the areas of smaller triangles help in finding the total area of the larger triangle?

### Tip
In geometry problems involving intersecting lines and given areas, try to express unknown areas in terms of the known areas using ratios or similar triangles.

In triangle PQR, point K is chosen on side PQ, and point L is chosen on side QR. Segments PL and KR intersect at point T. What is the area of triangle PQR if S_{PKT} = 9, S_{PDR} = 10, and S_{RTL} = 11?

Solve the problem of finding the area of triangle PQR when points K and L are on sides PQ and QR, intersecting at point T. Given areas S_{PKT} = 9, S_{PDR} = 10, and S_{RTL} = 11, use geometric principles and area ratios to determine the total area of triangle PQR. Suitable for Grades 10-12.

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