Answer:
206.35 square units.
Step-by-step explanation:
We have been given a triangular pyramid. We are asked to find total surface area of our given pyramid.
[tex]\text{Total surface area of pyramid}=A+(\frac{3}{2}\times b\times h)[/tex], where,
A = Area of base of pyramid,
b = Base of one of faces,
h = Height of one of faces.
[tex]\text{Area of base}=\frac{1}{2}\times \frac{\sqrt{3}}{2}\times 12\times 12[/tex]
[tex]\text{Area of base}=\frac{1}{4}\times \sqrt{3}\times 144[/tex]
[tex]\text{Area of base}=\sqrt{3}\times 36[/tex]
[tex]\text{Total surface area of pyramid}=36\sqrt{3}+(\frac{3}{2}\times b\times h)[/tex]
We know that height of an isosceles triangle is [tex]h=\sqrt{\text{One of equal side}^2-\frac{\text{base}^2}{4}}[/tex].
[tex]h=\sqrt{10^2-\frac{12^2}{4}}[/tex]
[tex]h=\sqrt{100-\frac{144}{4}}[/tex]
[tex]h=\sqrt{100-36}[/tex]
[tex]h=\sqrt{64}[/tex]
[tex]h=8[/tex]
[tex]\text{Total surface area of pyramid}=36\sqrt{3}+(\frac{3}{2}\times 12\times 8)[/tex]
[tex]\text{Total surface area of pyramid}=36\sqrt{3}+(3\times 48)[/tex]
[tex]\text{Total surface area of pyramid}=36\sqrt{3}+(144)[/tex]
[tex]\text{Total surface area of pyramid}=62.353829072479+(144)[/tex]
[tex]\text{Total surface area of pyramid}=206.3538\approx 206.35[/tex]
Therefore, the total surface area of our given pyramid is 206.35 square units.