The problem involves finding the area of the triangle shown in the image. Here's the solution:

Given Information:

• Base (AC) = $9.5 \, \text{m}$
• Height (AB) = $8.7 \, \text{m}$
• The triangle is labeled as $\triangle ABC$, with $AB$ as the height perpendicular to $AC$, the base.

Formula for the area of a triangle:

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

Substituting the values:

$\text{Area} = \frac{1}{2} \times 9.5 \, \text{m} \times 8.7 \, \text{m}$

Step-by-Step Calculation:

$\text{Area} = \frac{1}{2} \times 82.65 \, \text{m}^2$ $\text{Area} = 41.325 \, \text{m}^2$

Final Answer:

$\text{A: } 41.33 \, \text{m}^2 \, (\text{rounded to two decimal places})$

Let me know if you'd like further clarification! 😊

Expansion Questions:

1. What is the significance of using perpendicular height in the area formula?
2. How would the calculation change if the base or height were doubled?
3. Can you find the perimeter of the triangle using the given sides?
4. What real-world applications require calculating the area of a triangle?
5. How does the Pythagorean theorem relate to this triangle (if applicable)?

Tip:

Always ensure the base and height are perpendicular to use the area formula correctly!