How To Find The Surface Area Of A Triangular Pyramid

Surface Area of a Pyramid

The lateral surface area of a regular pyramid is the sum of the areas of its lateral faces.

The full surface surface area of a regular pyramid is the sum of the areas of its lateral faces and its base.

The full general formula for the lateral surface area of a regular pyramid is $L . Southward . A . = \frac{1}{2} p l$ where $p$ represents the perimeter of the base and $l$ the slant superlative.

Example 1:

Observe the lateral surface surface area of a regular pyramid with a triangular base of operations if each border of the base measures $8$ inches and the slant acme is $five$ inches.

The perimeter of the base of operations is the sum of the sides.

$p = iii (8) = 24 inches$

$L . S . A . = \frac{ane}{two} (24) (five) = sixty {inches}^{ii}$

The general formula for the total surface area of a regular pyramid is $T . Southward . A . = \frac{1}{ii} p l + B$ where $p$ represents the perimeter of the base of operations, $50$ the slant elevation and $B$ the surface area of the base of operations.

Instance 2:

Discover the total surface area of a regular pyramid with a foursquare base if each border of the base measures $xvi$ inches, the slant height of a side is $17$ inches and the altitude is $15$ inches.

The perimeter of the base is $4 s$ since it is a square.

$p = 4 (16) = 64 inches$

The expanse of the base is ${south}^{ii}$ .

$B = {sixteen}^{2} = 256 {inches}^{2}$

$\begin{array}{l} T . S . A . = \frac{1}{ii} (64) (17) + 256 \\ = 544 + 256 \\ = 800 {inches}^{2} \end{array}$

There is no formula for a surface area of a not-regular pyramid since slant height is non defined. To notice the area, find the area of each face and the surface area of the base and add them.