First, let's find the height of the triangular pyramid using the Pythagorean theorem. The height of the triangle is found by using the formula:
h = sqrt(12^2 - (10/2)^2)
h = sqrt(144 - 25)
h = sqrt(119)
h ≈ 10.91m
Now, we can calculate the total surface area of the pyramid. The formula for the surface area of a triangular pyramid is:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, let's find the base area of the equilateral triangle:
Base Area = (1/2) * base * height
Base Area = (1/2) * 10m * 8.7m
Base Area = 43.5m^2
Next, let's find the slant height using the Pythagorean theorem:
Slant Height = sqrt(10^2 + 10.91^2)
Slant Height = sqrt(100 + 119)
Slant Height = sqrt(219)
Slant Height ≈ 14.80m
Now, we can calculate the surface area of the pyramid:
Surface Area = 43.5m^2 + (1/2) * 10m * 14.80m
Surface Area = 43.5m^2 + 74m^2
Surface Area = 117.5m^2
Therefore, the surface area of the triangular pyramid is approximately 117.5 square meters.
A net of a triangular pyramid is shown below. The base is equilateral and the faces are congruent.
What is the surface area, in square meters, of the pyramid?
10m is the side of the triangle, 8.7m is the middle of the triangle and 12m is the pyramid
1 answer