A regular square pyramid has base area of 144in² and a slant height of 18 in. Find its surface area.

The total surface area is the sum of the areas of the square base and the four triangular faces. Using b for the base length and h for the triangle height, the area is ...

SA = b² +4(1/2)bh = b(b +2h)

For the base of 8 inches and the height of 5 inches, the total area is ...

SA = (8 in)(8 in + 2·5 in) = 8·18 in²

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✒MATHEMATICS

SOLUTION :

Formula for surface area of a regular square pyramid is:

[tex]{\boxed{{\sf{S.A = A + \frac{1}{2} \: ps }}}}[/tex]

Where,

A = area of base
P = perimeter of base
S = Slant height

If the base is a square with area (A) of 144 in², length of each side of base is:

A = a × a
144 = a²
a = √144
a = 12 in

Perimeter (P)

P = 4 × a
P = 4 × 12
P = 48 in

With A = 144 in², p = 48, and s = 18 in, surface area of the given square pyramid is:

S.A = A + 1/2 ps
S.A = 143 + 1/2 (48)(18)
S.A = 144 + 432
S.A = [tex]{\boxed{\green{\sf{576\: in²}}}}[/tex]

ANSWER :

Therefore, in, surface area of the given square pyramid is 576 in².

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