A triangle pyramids measurement are 10, 10.6, 14, and twelve. What is the surface area of the rectangular pyramid?

Answer 1

To Calculate the surface area of the triangular pyramid, first we need to calculate the base area and the lateral surface area.

The base of the triangular pyramid is a triangle with sides of lengths 10, 10.6, and 14. We can calculate the semiperimeter of the triangle using the formula:

s = (10 + 10.6 + 14) / 2
s = 17.3

Now, using the semiperimeter and the lengths of the sides, we can calculate the area of the base triangle using Heron's formula:

Area = √[s(s - 10)(s - 10.6)(s - 14)]
Area = √[17.3(17.3 - 10)(17.3 - 10.6)(17.3 - 14)]
Area = √[17.3 * 7.3 * 6.7 * 3.3]
Area = √(4836.049)
Area ≈ 69.52

The lateral surface area of the triangular pyramid can be calculated by finding the area of each of the three triangular faces and then summing them up.

Let's calculate the lateral surface area of one triangular face using the formula:

lateral surface area = (1/2) * base perimeter * slant height
slant height = 12

lateral surface area = (1/2) * (10 + 10.6 + √(10^2 + 12^2)) * 12
lateral surface area = (1/2) * (30.6 + √(100 + 144)) * 12
lateral surface area = (1/2) * (30.6 + √244) * 12
lateral surface area = (1/2) * (30.6 + 15.62) * 12
lateral surface area = (1/2) * 46.22 * 12
lateral surface area = 277.32

Therefore, the total surface area of the triangular pyramid = base area + lateral surface area
Total surface area = 69.52 + 277.32
Total surface area ≈ 346.84

So, the surface area of the rectangular pyramid is approximately 346.84.