MATH SOLVE

7 months ago

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

Accepted Solution

A:

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

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