At the base of the pyramid lies a right-angled triangle with a hypotenuse of 12 cm and an angle of 60 degrees.

At the base of the pyramid lies a right-angled triangle with a hypotenuse of 12 cm and an angle of 60 degrees. The height of the pyramid is 6 cm. Calculate its volume.

We find the legs through trigonometry: a / 12 = sin (60) => a = 12 * √ (3) / 2 = 6 * √ (3) b / 12 = cos (60) => b = 12/2 = 6 Area bases: S = a * b / 2 => S = 6 * 6 * √ (3) / 2 = 18 * √ (3) Volume: V = (1/3) * S * h => V = (1 / 3) * 18 * √ (3) * 6 => V = 36 * √ (3)
Answer: 36 * √ (3) cm ^ 3