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The problem asks to calculate the area of the triangle given a side length of 6 cm and an angle of 41°. 

To find the area of a triangle when two sides and the included angle are known, we use the following formula:

\[
\text{Area} = \frac{1}{2} \times a \times b \times \sin(\theta)
\]

In this case, one of the sides (6 cm) is given, and the angle is 41°. Since the triangle is isosceles (as shown by the markings on the two sides), the two equal sides are both 6 cm. Thus:

\[
\text{Area} = \frac{1}{2} \times 6 \times 6 \times \sin(41^\circ)
\]

Let's calculate the area step by step:

1. First, calculate \(\sin(41^\circ)\). Using a calculator:
   \[
   \sin(41^\circ) \approx 0.6561
   \]

2. Now plug it into the formula:
   \[
   \text{Area} = \frac{1}{2} \times 6 \times 6 \times 0.6561 = \frac{1}{2} \times 36 \times 0.6561 = 11.810
   \]

3. Rounding to the nearest 0.1 cm²:
   \[
   \text{Area} \approx 11.8 \, \text{cm}^2
   \]

Thus, the area of the triangle is approximately **11.8 cm²**.

Would you like further clarification, or do you have any questions? Here are 5 related questions to deepen your understanding:

1. How would the area change if the angle were larger?
2. Can you use a different method to calculate the area of this triangle?
3. What is the significance of using the sine function in the area formula?
4. How would you find the height of the triangle using trigonometry?
5. Can you calculate the perimeter of the triangle using the given information?

**Tip**: When solving problems involving trigonometry, make sure your calculator is in the correct mode (degrees or radians) based on the problem!

Work out the area of the triangle correct to the nearest 0.1 cm². Given that one side of the triangle is 6 cm and the angle between the two equal sides is 41°.

Learn how to calculate the area of a triangle when given two equal sides of 6 cm each and an included angle of 41°. This problem explores key trigonometric concepts such as using the sine rule to find the area of a triangle. Suitable for students in Grades 8-10.

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