The image shows a geometry problem involving a triangular pyramid, and the task seems to be calculating the surface area of the pyramid, given various dimensions.

From the image, the pyramid's base is an equilateral triangle, with each side measuring 22 cm. The height of each triangular face is 18 cm. The multiple-choice answers are given as:

• A. 1584 cm²
• B. 792 cm²
• C. 642 cm²
• D. 784 cm²

To calculate the surface area of a triangular pyramid:

1. Area of the Base (A₁): The base is an equilateral triangle, and the formula to calculate its area is: $A_{\text{base}} = \frac{\sqrt{3}}{4} s^2$ where $s$ is the side length of the equilateral triangle (22 cm).

2. Area of the Triangular Faces (A₂): The pyramid has three lateral faces, each of which is a triangle. The area of each face can be found using: $A_{\text{face}} = \frac{1}{2} \times \text{base} \times \text{height}$ where the base is 22 cm and the height is 18 cm for each triangular face.

3. Total Surface Area: The total surface area is the sum of the area of the base and the areas of the three triangular faces: $A_{\text{total}} = A_{\text{base}} + 3 \times A_{\text{face}}$

Let me calculate that for you now.The total surface area of the triangular pyramid is approximately $803.58 \, \text{cm}^2$.

Looking at the multiple-choice options, the closest answer is:

• D. 784 cm²

Would you like more details on the steps or have any questions? Here are 5 related questions to explore:

1. How do you calculate the area of an equilateral triangle?
2. Why is the formula for the area of a triangle $\frac{1}{2} \times \text{base} \times \text{height}$?
3. How would the surface area change if the side length of the base was different?
4. What if the triangular faces had different heights?
5. How is the surface area of other polyhedrons calculated?

Tip: When working with equilateral triangles, remember that all sides and angles are equal, which simplifies many calculations like area and perimeter.