# Total Surface Area of Regular Pyramid Calculator

Regular pyramid has a base of regular polygon. It can be square, rectangle, triangle or any other polygon. It is usually named after its base. The meeting point or apex of the pyramid is not necessarily to held right above centre of the base. Total surface area refers to the total area that the object occupies. It is the total area covered inside the object. Find the total surface area of regular pyramid from the known values of lateral surface area and area of base.

Regular pyramid has a base of regular polygon. It can be square, rectangle, triangle or any other polygon. It is usually named after its base. The meeting point or apex of the pyramid is not necessarily to held right above centre of the base. Total surface area refers to the total area that the object occupies. It is the total area covered inside the object. Find the total surface area of regular pyramid from the known values of lateral surface area and area of base.

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#### Formula:

S_{L} = (1 / 4) x n x Base Length x √(4b^{2} - Base Length^{2})
S_{B} = Semiperimeter x Radius
S = S_{L} + S_{B}
**Where,**
S = Total Surface Area (TSA)
S_{B} = Area of Base
S_{L} = Lateral Surface Area (LSA)
n = Number of Sides
b = Lateral Edge
### Example:

A 3 sided pyramid has a base length of 10 cm, lateral edge of 6 cm and radius of 15 cm and semiperimeter of 20. What is its LSA?

#### Solution:

S_{L} = (1 / 4) x 3 x 10 x √(4 x 6^{2} - 10^{2})

= 49.7494 cm^{2}

S_{B} = 20 x 15

= 300 cm^{2}

S = 49.7494+ 300

= 349.7494cm^{2}