A triangular pyramid has a base whose sides are 5 cm, 7 cm, and 7.5 cm. If the height of the pyramid is 10 cm, what is the volume of the pyramid?
Volume of a pyramid = (1/3)*base area*height
Using Heron's formula for area of a triangle we have:
semi-perimeter: s = (5 + 7 + 7.5)/2 = 9.75cm
base area = sqrt[s*(s-5)*(s-7)*(s-7.5)] ≈ 16.928 cm2
volume = 16.928*10 = 169.28 cm3