A Triangular Pyramid is a pyramid having a triangular base. The area of the surfaces of the object is called its surface area. The

surface area of a pyramid in square units. The triangular pyramid is one third of a

triangular prism of equal base and altitude.

The length of the triangular base is 'a' and 'H' is the height, distance from the base to the apex, 'h' be the apothem length

and '$l$' is the slant height.Triangular Pyramid Formula :

Area of Base(A) =

$\frac{1}{2}$ * a * h

Surface Area of Triangular Pyramid = (

$\frac{1}{2}$ * a * h) + (

$\frac{3}{2}$a$l$) = A + (

$\frac{3}{2}$a$l$)

**Formula:**

SA = A + $\frac{3}{2}$**a$l$**

Where,

SA = Surface area of triangular pyramid

A = Area of base

a = Side of the triangular base.

$l$ = Slant height.

Example:Find the surface area of a triangular pyramid with the given apothem length 3, side 4, height 5 and the slant height 6.

**Solution:**

Step 1:Apothem length (h) = 3

Side of base (a) = 4

Height of pyramid (H) = 5

Slant height ($l$) = 6

Step 2: Find the area of the base.

Area of the base(A) =

$\frac{1}{2}$ * a * h =

$\frac{1}{2}$ * 4 * 3 = 6

=> A = 6

Step 3: Find the surface area of pyramid.

Surface Area of Pyramid = A +

$\frac{3}{2}$a$l$

SA = 6 +

$\frac{3}{2}$ * 4 * 6

= 6 + 36

= 42

Hence surface area of the triangular pyramid is 42 units.

**answer**