At the base of the pyramid lies a triangle with sides of 5, 6 and 8 cm, and all the side edges of the pyramid are inclined

At the base of the pyramid lies a triangle with sides of 5, 6 and 8 cm, and all the side edges of the pyramid are inclined to the plane of the base at an angle of 45 °. Calculate the volume of the pyramid

You need to calculate the S of the base using Heron’s formula, and then R.
Let’s write the formula for the radius:
R = a * b * c / 4 * S.
But if you read the task, then we can calculate the volume of the pyramid.
It turns out that we need a formula:
V = R * S / 3;
It turns out that: V = a * b * c / 12;
Answer: V = 20;