Answer:
The lateral surface area is 1449.58 cm².
The total surface area is 2114.69 cm².
The volume is 5948.94 cm³.
Step-by-step explanation:
The question is:
Calculate the lateral area, total and volume of a hexagonal pyramid of 16 cm of basic edge and 28 cm of lateral edge. Answer question 2.
Solution:
Consider the diagram of the hexagonal pyramid.
It is provided that:
Base = a = 16 cm
Lateral height = b = 28 cm
Compute the length of Ap = h using the Pythagoras theorem as follows:
[tex]b^{2}=(\frac{a}{2})^{2}+h^{2}\\\\h^{2}=b^{2}-(\frac{a}{2})^{2}\\\\h=\sqrt{b^{2}-(\frac{a}{2})^{2}}\\\\=\sqrt{28^{2}-8^{2}}\\\\=\sqrt{720}[/tex]
Compute the lateral surface area as follows:
[tex]LSA=3a\sqrt{h^{2}+\frac{3a^{2}}{4}}=(3\cdot 16)\sqrt{720+\frac{3\cdot 16^{2}}{4}}=1449.58[/tex]
Thus, the lateral surface area is 1449.58 cm².
Compute the total surface area as follows:
[tex]TSA=\frac{3\sqrt{3}}{2}a^{2}+LSA=\frac{3\sqrt{3}}{2}\cdot16^{2}+1449.58=2114.69[/tex]
Thus, the total surface area is 2114.69 cm².
Compute the volume as follows:
[tex]\text{Volume}=\frac{\sqrt{3}}{2}\cdot a^{2}h=\frac{\sqrt{3}}{2}\times 16^{2}\times \sqrt{720}=5948.94[/tex]
Thus, the volume is 5948.94 cm³.
