Answer:
T.A. = 144 + 36√3
Step-by-step explanation:
The pyramid has a regular triangle for a base. The other three faces are isosceles triangles.
The height of base can be found by dividing it into two right triangles. We can either use properties of a 30-60-90 triangle, or use Pythagorean theorem.
h = 6√3
So the area of the base is:
A = 1/2 bh
A = 1/2 (12)(6√3)
A = 36√3
Similarly, the height of the three isosceles triangles can be found by dividing them into two right triangles and using Pythagorean theorem.
h = √(10² - 6²)
h = 8
So the area of the isosceles triangles is:
A = 1/2 bh
A = 1/2 (12)(8)
A = 48
So the total surface area of the pyramid is:
T.A. = 3(48) + 36√3
T.A. = 144 + 36√3
