The base of a triangular pyramid is a triangle with corners at (7 ,5 )(7,5), (6 ,9 )(6,9), and (3 ,4 )(3,4). If the pyramid has a height of 4 4, what is the pyramid's volume?

1 Answer
Jun 9, 2018

color(crimson)("Volume of Pyramid " V_p = (1/3) * A_b * h = 11.36 " cubic units"Volume of Pyramid Vp=(13)Abh=11.36 cubic units

Explanation:

color(violet)("Volume of Pyramid " V_p = (1/3) * A_b * hVolume of Pyramid Vp=(13)Abh

Area of base triangle " A_b = sqrt(s (s-a) (s-b) (s-c)), " using Heron's formula

A(7,5), B(6,9), C(3,4), h = 4

a = sqrt((6-3)^2 + (9-4)^2) = 5.83

b = sqrt((7-3)^2 + (5-4)^2) = 4.12

c = sqrt((6-7)^2 + (9-5)^2) = 4.12

It's an isosceles triangle with sides b & c equal.

"Semi-perimeter " s = (a + b + c) / 2

s = (5.83 + 4.12 + 4.12) / 2 ~~ 7.04

A_b = sqrt(7.04 * (7.04 - 5.83) * (7.04 - 4.12) * (7.04 - 4.12)) = 8.52

color(crimson)("Volume of Pyramid " V_p = (1/3) * A_b * h = (1/3) * 8.52 * 4 = 11.36 " cubic units"