Question

Find the surface area of the figure below. (Triangle: 10cm, a little square w 9cm, 9cm)
A. 261 cm^{2}
B. 270 cm^{2}
C. 441 cm^{2}
D. 810 cm^{2}

Answer 1

To find the surface area of the figure, we need to calculate the area of the triangle and the square and then sum them up.

1. **Area of the Triangle:**
- The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
- Assuming the triangle has a base of 10 cm and height of 10 cm (not specified, but given that "triangle: 10 cm" probably refers to its dimensions), we can calculate:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \text{ cm} \times 10 \text{ cm} = \frac{1}{2} \times 100 \text{ cm}^2 = 50 \text{ cm}^2
\]

2. **Area of the Square:**
- The formula for the area of a square is \( \text{Area} = \text{side}^2 \). Here, the side length is 9 cm.
\[
\text{Area}_{\text{square}} = 9 \text{ cm} \times 9 \text{ cm} = 81 \text{ cm}^2
\]

3. **Total Surface Area:**
- Now we add the areas of both the triangle and the square:
\[
\text{Total Surface Area} = \text{Area}_{\text{triangle}} + \text{Area}_{\text{square}} = 50 \text{ cm}^2 + 81 \text{ cm}^2 = 131 \text{ cm}^2
\]

Since the totals given in the options (A. 261 cm², B. 270 cm², C. 441 cm², D. 810 cm²) do not match, it's crucial to consider if there may be additional features or dimensions not addressed in this calculation. Let's make sure the areas calculated align with any specific constraints or intended measurements.

Based on the provided information, there isn't enough context for why it would equal any of the provided answers. Thus, we find our calculated surface area to be **131 cm²**, which does not match any of the supplied options.

If any additional details need clarification, please provide them to adjust the calculations accordingly.