Find the surface area of the triangle pyramid represented by the given net fourteen point seven feet seventeen feet and thirteen point eight feet

Answer 1

The surface area of a triangular pyramid can be found by adding the areas of each of the triangular faces.

In this case, we have a triangular pyramid with three triangular faces. The lengths of the sides of the base triangle are 14.7 feet, 17 feet, and 13.8 feet.

To find the area of the base triangle, we can use Heron's formula:

s = (14.7 + 17 + 13.8)/2 = 22.75

Area of base triangle = √(s*(s-14.7)*(s-17)*(s-13.8))
= √(22.75*(22.75-14.7)*(22.75-17)*(22.75-13.8))
= √(22.75*7.05*5.75*8.95)
= √(910.482)
≈ 30.18 square feet

Now, we need to find the area of the three triangular faces, which are all congruent. The height of the pyramid is the perpendicular distance from the apex to the base triangle. We can find the height using the Pythagorean theorem:

height^2 = 17^2 - (14.7/2)^2
height ≈ √(289 - 53.69)
height ≈ √235.31
height ≈ 15.34 feet

Now, we can find the area of one triangular face using the formula:

1/2 * base * height = 1/2 * 14.7 * 15.34 = 112.83 square feet

Since all three triangular faces are congruent, the total surface area can be calculated as:

Surface area = base area + 3(triangular face area)
Surface area = 30.18 + 3(112.83)
Surface area ≈ 368.67 square feet

Therefore, the surface area of the triangular pyramid represented by the given net is approximately 368.67 square feet.