At the base of the triangular pyramid lies an isosceles triangle with sides

At the base of the triangular pyramid lies an isosceles triangle with sides 17, 17, and 16 inches. Find the volume of the pyramid if its height is 5 dm.

To find out the volume of a given triangular pyramid, we use the formula: V = Sbasn * h / 3 = b * √ (4a ^ 2 – b ^ 2) * h / (4 * 3), where b is the base of the triangle (b = 16 dm) ; a – the length of each of the two sides (a = 17 dm); h is the height of a given triangular pyramid (h = 5 dm).

Let’s calculate: V = b * √ (4a ^ 2 – b ^ 2) * h / (4 * 3) = 16 * √ (4 * 17 ^ 2 – 16 ^ 2) * 5 / (4 * 3) = 4 * √900 * 5/3 = 4 * 30 * 5/3 = 4 * 10 * 5 = 200 dm3.

Answer: The volume of a given triangular pyramid is 200 dm3.