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What is the lateral area of this regular octagonal pyramid?

A. 84.9 cm^2

B. 120 cm^2

C. 169.7 cm^2

D. 207.8 cm^2

arota21  May 23, 2017

Best Answer 

 #1
avatar+4777 
+1

The sum of the areas of all 8 triangles is the lateral area.

And, each of these triangles are the same size.

So...

lateral area = 8 * area of one of these triangles

lateral area = 8 * (1/2) * base * height

 

 

From the Pythagorean theorem:

62 + 62 = height2          \(\rightarrow \quad \text{height} = \sqrt{72}=6\sqrt2\)

 

 

lateral area = 8 * (1/2) * 5 * 6√2

lateral area = 120√2     ≈     169.7   cm2

hectictar  May 23, 2017
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2+0 Answers

 #1
avatar+4777 
+1
Best Answer

The sum of the areas of all 8 triangles is the lateral area.

And, each of these triangles are the same size.

So...

lateral area = 8 * area of one of these triangles

lateral area = 8 * (1/2) * base * height

 

 

From the Pythagorean theorem:

62 + 62 = height2          \(\rightarrow \quad \text{height} = \sqrt{72}=6\sqrt2\)

 

 

lateral area = 8 * (1/2) * 5 * 6√2

lateral area = 120√2     ≈     169.7   cm2

hectictar  May 23, 2017
 #2
avatar+77131 
+3

 

 

The lateral  area will be comprised of 8 congruent triangles

 

The slant height  of each triangle  = sqrt (6^2 + 6^2)  = sqrt (72)  = 6sqrt (2) cm

 

And the base of each triangle  = 5 cm

 

So.....the total lateral  area  =

 

8 * (1/2) (base) (slant height)  =

 

8 (1/2) (5) (6sqrt(2) ) ≈  169.7 cm ^2

 

 

 

cool cool cool

CPhill  May 23, 2017

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