Question

Calcula el area lateral,total y volumen de una piramide hexagonal de 16 cm de arista basica y 28 cm de arista lateral Responde la pregunta 2.

Answer 1

The lateral surface area is 1449.58 cm².

The total surface area is 2114.69 cm².

The volume is 5948.94 cm³.

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:

`b^(2)=((a)/(2))^(2)+h^(2)\\\\h^(2)=b^(2)-((a)/(2))^(2)\\\\h=\sqrt{b^(2)-((a)/(2))^(2)}\\\\=\sqrt{28^(2)-8^(2)}\\\\=√(720)`

Compute the lateral surface area as follows:

`LSA=3a\sqrt{h^(2)+(3a^(2))/(4)}=(3\cdot 16)\sqrt{720+(3\cdot 16^(2))/(4)}=1449.58`

Thus, the lateral surface area is 1449.58 cm².

Compute the total surface area as follows:

`TSA=(3√(3))/(2)a^(2)+LSA=(3√(3))/(2)\cdot16^(2)+1449.58=2114.69`

Thus, the total surface area is 2114.69 cm².

Compute the volume as follows:

`\text{Volume}=(√(3))/(2)\cdot a^(2)h=(√(3))/(2)* 16^(2)* √(720)=5948.94`

Thus, the volume is 5948.94 cm³.