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# help plz

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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

May 23, 2017

#1
+7352
+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

May 23, 2017

#1
+7352
+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
#2
+98196
+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

May 23, 2017
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