Find the volume of the regular hexagonal pyramid if the lateral edge is 15 feet.

Volume of the given pyramid = 1122.37 cubic feet

Step-by-step explanation:

Volume of the regular hexagonal pyramid =

Measure of internal angle of a polygon =

Here, n = number of sides of the polygon

For a hexagon, n = 6

Measure of interior ∠C =

                                       = 120°

Measure of ∠BCD =

                              = 60°

By applying tangent rule in ΔCED,

tan(∠ECD) =

tan(60°) =

DE = feet

And cos(60°) =

CD = 12 feet

Area of ΔBCD =

                        =  

                        = feet

Area of hexagonal Base of the pyramid =

                                                                  = 216√3 square feet

Since, lateral height of the pyramid (AC) = 15 feet

By applying Pythagoras theorem in ΔADC,

AC² = AD² + CD²

(15)² = AD² + (12)²

AD =

AD = 9 feet

Volume of the given pyramid =

                                                 = 648√3 cubic feet

                                                 = 1122.37 cubic feet

b

step-by-step explanation: