-Use the drawing to explain the following theorem.
"The lateral area L of a regular pyramid with slant height of length l and perimeter P for the base is given by ."
[Note: Except for the number of sides for the base, the proof (argument) will not change
for another regular polygon.]
Given: Regular polygon with slant height of length l
and length s for each side of the base
Prove:

Question

-Use the drawing to explain the following theorem.
"The lateral area L of a regular pyramid with slant height of length l and perimeter P for the base is given by  ."
[Note: Except for the number of sides for the base, the proof (argument) will not change
for another regular polygon.]
Given: Regular polygon with slant height of length l
and length s for each side of the base
Prove:

Quizplus · Accepted Answer

The Answer is The faces of the regular polygon are congruent triangles. For each face, the altitude has
length l while the corresponding base length is s. Thus, the area of each of the n faces is

The faces of the regular polygon are congruent triangles. For each face, the altitude has length l while the corresponding base length is s. Thus, the area of each of the n faces is . The lateral area L is the sum of areas of all lateral faces. That is, , Because , the formula for the lateral area becomes .

. The lateral area L is the sum of areas of all lateral faces. That is, The faces of the regular polygon are congruent triangles. For each face, the altitude has length l while the corresponding base length is s. Thus, the area of each of the n faces is . The lateral area L is the sum of areas of all lateral faces. That is, , Because , the formula for the lateral area becomes .

,

Because

, the formula for the lateral area becomes The faces of the regular polygon are congruent triangles. For each face, the altitude has length l while the corresponding base length is s. Thus, the area of each of the n faces is . The lateral area L is the sum of areas of all lateral faces. That is, , Because , the formula for the lateral area becomes .

.

-Use the Drawing to Explain the Following Theorem