A pyramid is formed on a \(6\times 8\) rectangular base. The four edges joining the apex to the corners of the rectangular base each have length 13.What is the volume of the pyramid?

Logic Jun 22, 2019

#1**+1 **

First, draw a diagram. Label the information that has been presented to you in the problem, then male the steps and moves.

Drawing an altitude from the top of the base to the bottom, we should cleverly use the six units and eight units. By the Pythagorean Theorem, the diagonal length is ten inches. Now, take half of the diagonal, which is five, and point it towards the corner. Here, we should see a 5-12-13 triangle, and thus the height is twelve inches. The volume of the pyramid is \(\frac{B*h}{3}=\frac{48*12}{3}=48*4=\boxed{192}\) squared units(units squared).

tertre Jun 22, 2019

#1**+1 **

Best Answer

First, draw a diagram. Label the information that has been presented to you in the problem, then male the steps and moves.

Drawing an altitude from the top of the base to the bottom, we should cleverly use the six units and eight units. By the Pythagorean Theorem, the diagonal length is ten inches. Now, take half of the diagonal, which is five, and point it towards the corner. Here, we should see a 5-12-13 triangle, and thus the height is twelve inches. The volume of the pyramid is \(\frac{B*h}{3}=\frac{48*12}{3}=48*4=\boxed{192}\) squared units(units squared).

tertre Jun 22, 2019