Find the lateral area surface area and volume of the pentago

Find the lateral area, surface area, and volume of the pentagonal pyramid. (a) Apothem of the base, a (b) Perimeter of the base, p (c) Area of the base, B (d) Lateral area of the solid, L (c) Surface area of the solid, T (f) Volume of the solid, V

Solution

The lateral area of a solid is defined as the combined area of all of its lateral faces. The lateral faces are the sides of the solid excluding the base and top. For a pentagonal pyramid, the lateral area is the combined area of the five triangular sides of the pyramid. To calculate this, you must find the areas of the triangular sides and add them together.

When base edge = 11.6 in and height = 15 in

Lateral Area = 492.77 in²(approx)

Surface Area when side faces are the same
= [Base Area] + 1/2 × Perimeter × [Side Length]

Base Area = 5/4tan(54°)a² = 231.51 in²

Hence Surface Area = 724.28 in²(approx)

(Volume) V=5/12tan(54°)ha² = 1157.54 in³ (approx)

apothem length of the pentagonal pyramid = 17in