To calculate the area of the triangle, we’ll use the formula for the area of a triangle with two sides and an included angle:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

where:

• $a$ and $b$ are the lengths of two sides,
• $C$ is the included angle between these sides.

From the image:

• The two equal sides are each 6 cm (an isosceles triangle),
• The included angle is $41^\circ$.

Step-by-Step Solution

1. Identify the values: $a = 6 \text{ cm}, \quad b = 6 \text{ cm}, \quad C = 41^\circ$

2. Use the formula: $\text{Area} = \frac{1}{2} \times 6 \times 6 \times \sin(41^\circ)$

3. Calculate $\sin(41^\circ)$: $\sin(41^\circ) \approx 0.6561$

4. Substitute and solve: $\text{Area} = \frac{1}{2} \times 6 \times 6 \times 0.6561$ $= \frac{1}{2} \times 36 \times 0.6561$ $= 18 \times 0.6561$ $\approx 11.81 \text{ cm}^2$

Final Answer

The area of the triangle is approximately 11.8 cm², rounded to the nearest 0.1 cm².

Would you like a further breakdown or have any questions?

Here are some related questions you might find useful:

1. How do you find the area of a triangle using side lengths and angles?
2. What is the significance of the sine function in trigonometry?
3. How can you find the area of other types of triangles (e.g., right triangles)?
4. What is the law of sines and how is it applied in triangle calculations?
5. How would you approach this if only one side and two angles were given?

Tip: Always check if the triangle is isosceles or equilateral, as it can simplify calculations by confirming equal sides or angles.