Use the image to answer the question. Find the surface area of the net given an equilateral triangle as the base.

numbers:
14.0 m
14.5 m
16.2 m

3 answers

To find the surface area of the net, we first find the area of the equilateral triangle by using the formula:

Area = (√3 / 4) * side length squared

Area = (√3 / 4) * 14.0^2
Area = (√3 / 4) * 196
Area = 169.686 m^2 (approximately)

There are three identical triangles in the net, so the total surface area is:

Surface Area = 3 * 169.686
Surface Area = 509.058 m^2

Therefore, the surface area of the net is approximately 509.058 m^2.
wrong
Apologies for the mistake. Let's try calculating the surface area of the net with the correct dimensions provided:

Given:
Base side length of equilateral triangle = 14.0 m
Height of the triangular prism = 14.5 m
Total height of the net = 16.2 m

To find the surface area of the net, we need to calculate the surface area of each individual shape and then sum them up:

1. Surface area of the equilateral triangle base:
Area = (√3 / 4) * side length^2
Area = (√3 / 4) * 14.0^2
Area = (√3 / 4) * 196
Area ≈ 151.29 m^2

2. Surface area of the three rectangular sides:
There are three sides (rectangles) in the net:
- Two rectangles with dimensions 14.0 m (side length of triangle) x 14.5 m (height)
- One rectangle with dimensions 14.0 m (base side) x 16.2 m (total height) - this is the back wall of the triangular prism.

Total surface area of the three rectangular sides:
= 2 * (14.0 * 14.5) + 14.0 * 16.2
= 406.0 m^2

Total Surface Area of the net:
= Area of Triangle Base + Surface Area of Three Rectangular Sides
= 151.29 + 406.0
= 557.29 m^2

Therefore, the surface area of the net is approximately 557.29 m^2.