1. What shape is it?
There are no rectangular faces, so this is a triangular pyramid.
As you can see on the formula chart, this formula is rather different compared to prisms and cylinders. One of the differences is the requirement of lateral height (l). This is the height from the base to the top of the pyramid measured along a face instead of through the middle of the shape. Since the sides are all triangles, they would add up into one big triangle, but would still follow the area formula, so that's where the 1/2 comes from. Also there is only one base.
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (s+s+s) * l + ((1/2) * b * h)
3. Plug in the numbers
S. A. = (1/2) * (5 + 5 + 5) * 7.1 + ((1/2) * 5 * 4.3)
4. Solve
That looks like alot, so let's break it down by using order of operations. The perimeter is easy with 15, and half that is 7.5.
S. A. = 7.5 * 7.1 + ((1/2) * 5 * 4.3)
Next, half of 5 is 2.5. S. A. = 7.5 * 7.1 + (5 * 4.3)
S. A. = 53.25 + 21.5
S. A. = 74.75 square feet
Let's try another.
This is a rectangular or square pyramid.
2. Write the formulas
General S. A. = (1/2) * P * l + B
Specific S. A. = (1/2) * (2b + 2h) * l + (b * h)
3. Plug in the numbers
S. A. = (1/2) * (2 * 9 + 2 * 9) * 9.2 + (9 * 9)
4. Solve
S. A. = (18) * 9.2 + (81)
S. A. = 165.6 + 81
S. A. = 246.6 square centimeters
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