Find the volume of this triangular pyramid to the nearest millimeters with the height 10mm, and bases 12mm, 8mm, and 7mm?

Answer 1

To find the volume of a triangular pyramid, you can use the formula:

Volume = (1/3) * base area * height

First, we need to find the area of the triangular base. We can use Heron's formula to find the area of an irregular triangle with sides of lengths 12mm, 8mm, and 7mm:

s = (12 + 8 + 7) / 2 = 13.5mm
Area = √[13.5 * (13.5 - 12) * (13.5 - 8) * (13.5 - 7)] = √[13.5 * 1.5 * 5.5 * 6.5] = √677.625 ≈ 26.018mm²

Now, we can find the volume of the triangular pyramid:

Volume = (1/3) * 26.018 * 10 = 86.72667 mm³

To the nearest millimeter, the volume of the triangular pyramid is approximately 87 mm³.