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Find the total area for the regular pyramid.

Find the total area for the regular pyramid.-example-1

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Answer:

206.35 square units.

Explanation:

We have been given a triangular pyramid. We are asked to find total surface area of our given pyramid.


\text{Total surface area of pyramid}=A+((3)/(2)* b* h), where,

A = Area of base of pyramid,

b = Base of one of faces,

h = Height of one of faces.


\text{Area of base}=(1)/(2)* (√(3))/(2)* 12* 12


\text{Area of base}=(1)/(4)* √(3)* 144


\text{Area of base}=√(3)* 36


\text{Total surface area of pyramid}=36√(3)+((3)/(2)* b* h)

We know that height of an isosceles triangle is
h=\sqrt{\text{One of equal side}^2-\frac{\text{base}^2}{4}}.


h=\sqrt{10^2-(12^2)/(4)}


h=\sqrt{100-(144)/(4)}


h=√(100-36)


h=√(64)


h=8


\text{Total surface area of pyramid}=36√(3)+((3)/(2)* 12* 8)


\text{Total surface area of pyramid}=36√(3)+(3* 48)


\text{Total surface area of pyramid}=36√(3)+(144)


\text{Total surface area of pyramid}=62.353829072479+(144)


\text{Total surface area of pyramid}=206.3538\approx 206.35

Therefore, the total surface area of our given pyramid is 206.35 square units.

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