Question

В основі піраміди трикутника зі сторонами 13 ,14,15 Н=10 ,знайти V-?

Answer 1

V = 1/3 * S осн * H

S осн = √р(р-а)(р-b)(p-c) 

p - полупериметр р=(a+b+c)/2=21

S=√21(21-13)(21-14)(21-15) = √21*8*7*6=√3*7*2*2*2*7*2*3=3*7*2*2=84

V=1/3 * 84 * 10 = 280 

Answer 2

Finding the Volume of a Pyramid

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

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

In this case, the base of the pyramid is a triangle with sides measuring 13, 14, and 15 units, and the height is given as 10 units. We need to find the volume of this pyramid.

To calculate the base area of the pyramid, we can use Heron's formula, which allows us to find the area of a triangle given the lengths of its sides. Heron's formula states:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.

Let's calculate the volume step by step:

1. Calculate the semi-perimeter of the triangle: - s = (13 + 14 + 15) / 2 = 21

2. Calculate the base area of the pyramid using Heron's formula: - Area = sqrt(21 * (21 - 13) * (21 - 14) * (21 - 15)) = sqrt(21 * 8 * 7 * 6) = sqrt(2112) ≈ 45.99

3. Calculate the volume of the pyramid using the formula: - V = (1/3) * base area * height = (1/3) * 45.99 * 10 = 153.3 cubic units

Therefore, the volume of the pyramid with a base triangle of sides 13, 14, and 15 units and a height of 10 units is approximately 153.3 cubic units.

Please note that the calculations provided are based on the information given and may vary slightly depending on the rounding of decimal places.