+36 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
+9466 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
+9466 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
+128475
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
