Question

Use the image to answer the question.

An illustration shows a triangular pyramid. The perpendicular height of the base measures 3.9 centimeters and its sides measure 4.5 centimeters. The slant height measures 3.5 centimeters.

Find the surface area of the solid figure with an equilateral triangle base.

(1 point)
cm2
Skip to navigation

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for the surface area of a triangular pyramid is:

Surface Area = (0.5 * base perimeter * slant height) + (base area)

First, let's calculate the base perimeter:
Base perimeter = 3 * side = 3 * 4.5 cm = 13.5 cm

Now, let's calculate the base area of an equilateral triangle:
Base area = (sqrt(3)/4) * side^2 = (sqrt(3)/4) * (4.5^2) = (sqrt(3)/4) * 20.25 = 8.78 cm^2

Now, plug in the values into the formula to find the surface area:
Surface Area = (0.5 * 13.5 * 3.5) + 8.78
Surface Area = 23.625 + 8.78
Surface Area = 32.405 cm^2

Therefore, the surface area of the triangular pyramid with an equilateral triangle base is 32.405 cm^2.