Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral triangle base.
(10ft,6ft,6ft,6ft,5.2ft.)(if i could put in a pic i would)
A. 106ft
B. 114ft
C. 122ft
D. 130ft
it doesn't work
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heres the rest put them together
To compute the surface area of a triangular pyramid with an equilateral triangle base, we need to find the area of the base and the area of the lateral faces.
First, let's find the area of the equilateral triangle base. We can use the formula for the area of an equilateral triangle:
Area = (side length^2 * √3) / 4
Given the side length of the equilateral triangle base is 10ft, we can calculate the area:
Area of base = (10^2 * √3) / 4
= (100 * 1.732) / 4
≈ 43.301ft (rounded to three decimal places)
Next, let's find the area of the four lateral faces of the pyramid. Each lateral face is a triangle, so we can calculate their areas using the formula:
Area = (base length * height) / 2
Given the dimensions of the lateral faces are (6ft, 6ft, 5.2ft), we can calculate the area of each face:
Area of each lateral face = (6 * 5.2) / 2
= 31.2 / 2
= 15.6ft
Since there are four lateral faces, the total area of the lateral faces is 4 * 15.6ft = 62.4ft.
Finally, we can compute the surface area of the triangular pyramid by adding the area of the base and the total area of the lateral faces:
Surface area = Area of base + Total area of lateral faces
≈ 43.301ft + 62.4ft
≈ 105.701ft
Rounded to the nearest integer, the surface area of the triangular pyramid is 106ft.
Therefore, the correct answer is:
A. 106ft.
you have the net.
You know how to calculate the area of triangles, right?
so do that, and add 'em up.