Question

ASAP What is the lateral area of this regular octagonal pyramid?? Explain your answer if you can plz thanks

Answer 1

Answer:

Hello! The correct answer is 298.7 $cm^{2}$

Step-by-step explanation:

I am just confirming!

Answer 2

The lateral area would be 298.7 cm².

The lateral area is the area of all of the lateral faces of the pyramid.  There are 8 triangles making up the lateral faces.  Each has a base of 6.6.  The formula for the area of a triangle is

A=1/2bh,

so we still need the height of the triangle.

The height of each lateral triangle is the slant height of the pyramid.  The slant height of the pyramid forms a right triangle with the height of the pyramid and the "radius" as it were of the pyramid.  Thus we use the Pythagorean theorem:

8²+8²=h²
64+64=h²
128=h²
√128=√(h²)
8√2 = h

Substituting this into our area formula we have:
A=1/2(6.6)(8√2)

We will go ahead and multiply this by 8, since there are 8 lateral faces:
LA=8(1/2)(6.6)(8√2)
LA = 298.7