The image shows a triangular pyramid where the lengths of its triangular faces and base are given. We need to find the surface area of this triangular pyramid. The pyramid's dimensions are as follows:

• The base is an equilateral triangle with side lengths of 13 yards.
• The slant height of the triangular face is 14 yards.
• The height of the triangular base is 11.3 yards.

To calculate the surface area of a pyramid, we need to add:

1. The area of the base (which is a triangle in this case).
2. The area of the lateral faces (there are three triangular faces, all with the same base and slant height).

Step 1: Find the area of the base.

Since the base is an equilateral triangle: $\text{Area of base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 13 \times 11.3 = 73.45 \text{ square yards}$

Step 2: Find the area of the three lateral faces.

Each lateral face is a triangle with a base of 13 yards and a height (slant height) of 14 yards: $\text{Area of one lateral face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 13 \times 14 = 91 \text{ square yards}$ Since there are three lateral faces: $\text{Total area of lateral faces} = 3 \times 91 = 273 \text{ square yards}$

Step 3: Add the areas together.

$\text{Total surface area} = \text{Area of base} + \text{Area of lateral faces} = 73.45 + 273 = 346.45 \text{ square yards}$

Thus, the surface area of the triangular pyramid is 346.45 square yards.

Would you like more details or have any other questions?

Related Questions:

1. How would the surface area change if the slant height increased by 2 yards?
2. Can you explain how to calculate the volume of this triangular pyramid?
3. What would happen to the surface area if the base was not equilateral?
4. How do you find the slant height if it's not provided?
5. How is surface area calculation different for a square pyramid compared to a triangular pyramid?

Tip:

Remember, for any pyramid, the surface area includes both the area of the base and the lateral faces. Ensure you account for the number of lateral faces correctly depending on the shape of the base!