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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

#1**+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:

6^{2} + 6^{2} = height^{2} \(\rightarrow \quad \text{height} = \sqrt{72}=6\sqrt2\)

lateral area = 8 * (1/2) * 5 * 6√2

lateral area = 120√2 ≈ 169.7 cm^{2}

hectictar May 23, 2017

#1**+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:

6^{2} + 6^{2} = height^{2} \(\rightarrow \quad \text{height} = \sqrt{72}=6\sqrt2\)

lateral area = 8 * (1/2) * 5 * 6√2

lateral area = 120√2 ≈ 169.7 cm^{2}

hectictar May 23, 2017

#2**+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

CPhill May 23, 2017