Given:
There is a figure given in the question
Required:
We need to find the surface area of given figure of pyramid
Explanation:
First we need to find the side of base square
use tan function
[tex]\begin{gathered} \tan30=\frac{SM}{DM} \\ \\ \frac{1}{\sqrt{3}}=\frac{6}{DM} \\ \\ DM=6\sqrt{3} \end{gathered}[/tex]
now to find the side of base square is
[tex]DC=2DM=12\sqrt{3}[/tex]
The surface area of pyramid is
[tex]TSA=\frac{1}{2}Pl+B[/tex]
where P is base of perimeter
l is the slant height which is 6 cm
B is the base area
now find P
[tex]P=4*12\sqrt{3}=48\sqrt{3}\text{ cm}[/tex]
now find B
[tex]B=12\sqrt{3}*12\sqrt{3}=432\text{ cm}^2[/tex]
now substitute all the values in the formula of Total surface area of pyramid
[tex]TSA=\frac{1}{2}Pl+B=\frac{1}{2}*48\sqrt{3}*6+432[/tex]
simplify as:
[tex]\begin{gathered} =249.4+432 \\ =681.4\text{ cm}^2 \end{gathered}[/tex]
Final answer:
Total surface area of given figure is 681.4 square cm
