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Which expression gives the area of triangle QRS?

A right triangle RSQ with base RQ of 9, hypotenuse RS of 15, and opposite QS of 11 with an angle at R of 20 degrees.

To solve this, we need to calculate the area of triangle \( QRS \). The general formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

For the right triangle \( QRS \), we know the base \( RQ = 9 \) and the opposite side \( QS = 11 \).

So the area of the triangle is:

\[
\text{Area} = \frac{1}{2} \times 9 \times 11 = 49.5
\]

The expression for the area of triangle \( QRS \) is:

\[
\frac{1}{2} \times 9 \times 11
\]

Would you like further details on how I arrived at the area?

Here are 5 related questions:
1. How is the area of a triangle calculated in different situations?
2. Can we use trigonometry to find the area in this triangle?
3. What is the significance of the hypotenuse in calculating the triangle's area?
4. How do the Pythagorean theorem and trigonometric ratios relate to right triangles?
5. Why is the area of a right triangle calculated differently from non-right triangles?

**Tip:** Always remember to confirm which sides are the base and height when using the area formula for triangles.

Understand how to calculate the area of triangle QRS with a base length of 9 and a height of 11, using the area formula for triangles. This problem involves applying the Pythagorean theorem in a right triangle context. Suitable for students in Grades 7-9.

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