Question

calcule a superfície total de um pirâmide triangular regular que tem 25 cm de aresta lateral e 8 cm de aresta da base.

Answer 1

Aresta lateral e L = 25cm
Aresta da base e a = 8cm

Area da base
~~~~~~~~~~~~
Ab = a^2 * \|3
..........._______
.................4

Ab = (8)^2 * \|3
.........________
...................4

Ab = 64 * \|3
..........______
................4

Ab = 16 * \|3 cm^2


Apotema da piramide
~~~~~~~~~~~~~~~~~~~
A^2 = L^2 - (a/2)^2

A^2 = (25)^2 - (8/2)^2

A^2 = 625 - (4)^2

A^2 = 625 - 16

A^2 = 609

A = \|609

A = 24,67cm

Area lateral
~~~~~~~~~~~
Al = 3 * (a * A/2)

Al = 3 * ( 25 * 24,67/2)

Al = 3 * ( 25 * 12,34)

Al = 3 * (308,90)

Al = 925,50 cm^2


Area total
~~~~~~~~~
At = Al + Ab

At = 925,50 + 16 * \|3 cm^2

At = 925,50 + 16(1,73) cm^2

At = 925,50 + 27,68 cm^2

At = 953,18cm^2