Answer:
- triangles: 24 ft²
- square: 9 ft²
- total surface area: 33 ft²
Explanation:
You want the lateral area, base area, and total area of a square pyramid with a base 3 ft on a side and a slant height of 4 ft.
Triangle area
The area of one triangle is ...
A = 1/2bh
A = 1/2(3 ft)(4 ft) = 6 ft²
Then the area of the four triangular faces is ...
area of triangles = 4×6 ft² = 24 ft²
Base
The area of the square base is ...
A = s²
A = (3 ft)² = 9 ft²
The area of the square base is 9 ft².
Total
The total surface area is the sum of the lateral area and the base area:
total surface area = area of triangles + area of square = 24 ft² +9 ft²
total surface area = 33 ft²
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