Let's solve the problem step by step to find the surface area of the triangular pyramid.
1. Calculate the area of one lateral face
The lateral faces of the pyramid are triangles. The area of a triangle can be determined using the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
We are given the base of each lateral face as 4 centimeters and the height as 12 centimeters. Hence, the area of one lateral face is:
[tex]\[ \text{Area} = \frac{1}{2} \times 4 \, \text{cm} \times 12 \, \text{cm} = \frac{1}{2} \times 48 \, \text{cm}^2 = 24 \, \text{cm}^2 \][/tex]
2. Calculate the total area of the lateral faces
A triangular pyramid has three lateral faces. Therefore, the total area of all three lateral faces is:
[tex]\[ \text{Total lateral faces area} = 3 \times 24 \, \text{cm}^2 = 72 \, \text{cm}^2 \][/tex]
3. Determine the total surface area of the pyramid
The surface area of the pyramid is the sum of the area of the base and the total area of the lateral faces. We are given the area of the base as 7 square centimeters. Therefore, the total surface area [tex]\(A\)[/tex] is:
[tex]\[ A = \text{base area} + \text{total lateral faces area} = 7 \, \text{cm}^2 + 72 \, \text{cm}^2 = 79 \, \text{cm}^2 \][/tex]
So, the surface area of the triangular pyramid is 79 square centimeters.
Thus, the correct answer is:
[tex]\[ \boxed{79 \, \text{square centimeters}} \][/tex]
or, according to the provided options:
B. 79 square centimeters
