The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
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Check the picture below.
the triangle is an isosceles, so it has twin legs, and a base bottom.
the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.
if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.
so, anyhow, the rest is just a matter of using the 30-60-90 rule.
that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.
the triangle is an isosceles, so it has twin legs, and a base bottom.
the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.
if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.
so, anyhow, the rest is just a matter of using the 30-60-90 rule.
that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.