Question

Find the total area for the regular pyramid
(please follow the answer set up in the picture)

Answer 1

T.A. = 144 + 36√3

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