Question

A right pyramid with a square base has a base edge length of 12 meters and slant height of 6StartRoot 2 EndRoot meters. The apothem is meters. The hypotenuse of ΔABC is the . The height is meters. The volume of the pyramid is cubic meters.

Answer 1

the apothem is 6

the hypotenuse of ABC is the slant height

the height is 6 meters

the volume of the pyramid is 288 cubic meters

Explanation:

Answer 2

Volume of the right pyramid = 288 m²

Explanation:

Volume of the pyramid =
`(1)/(3)* {\text{Area of the rectangular base}* height(h)`

From the ΔAOB,

By Pythagoras theorem,

AB² = AO² + OB²

(6√2)² = AO² + (6)²

72 = AO² + 36

AO = √(36) = 6 m

Since base of the pyramid is a square so area of the base = (Length × Width) = (side)²

Now volume of the pyramid =
`(1)/(3)[(Length)(width)]* height`

=
`(1)/(3)(12* 12)* 6`

= 288 m²

Therefore, volume of the right pyramid is 288 m².