14.0 m

16.2 m
14.5 m
Find the surface area of the net given an equilateral triangle as the base.
__ m2

1 answer

To find the surface area of the net, we first need to find the height of the equilateral triangle.

For an equilateral triangle, the height can be found using the formula h = √(3)/2 * s, where s is the length of one side of the equilateral triangle.

Given that the side length of the equilateral triangle is 14.0 m, we can calculate the height as:
h = √(3)/2 * 14.0
h = 12.1 m

Now we can find the surface area of one of the triangular faces of the net using the formula for the area of a triangle: A = (1/2) * base * height.

Since the base of the triangle is 14.0 m and the height is 12.1 m, we can calculate the area of one triangle face as:
A = (1/2) * 14.0 * 12.1
A ≈ 85.4 m^2

Since there are 3 identical triangular faces in the net, the total surface area of the net is:
Total Surface Area = 3 * 85.4
Total Surface Area ≈ 256.2 m^2

Therefore, the surface area of the net given an equilateral triangle as the base is approximately 256.2 m^2.
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