![]() So what is the surfaceĪrea of this one here? Well, it's gonna be fiveĬentimeters times two centimeters. Then add them together, the surface area ofĮach of these surfaces. Out the surface area of each of these sections and This net here is it's laid out all of the surfaces for us, and we just have to figure Is this thing's surfaceĪrea 40 square centimeters? Well, the good thing about Two centimeters tall, and it is two centimeters, This would be the top, and then the top would of course go on top of our rectangular prism. And then of course we have the top that's connected right over here. When we fold this side in, that's the side that's kind We fold this side in, that's the same color. When you fold this side in, right over here, that could be that. Right over here, this side right over here along When we fold up that side, that could be this side If I want, five centimeters, and that's of course the sameĪs that dimension up there. This dimension right over here, I can put the double hash marks You're gonna have your base that has a length of five centimeters. Start with a net like this and try to visualize the polyhedron that it actually represents,Īnd it looks pretty clear that this is going toīe a rectangular prism, but let's actually draw it. Now, they don't ask us toĭo this in the problem, but it's always fun to Pretty much all the rest of the edges are going Has the same number of hash marks, in this case, one, is also going to be two centimeters. So that's five centimetersĪnd that's five centimeters. And then these two over hereĪre also five centimeters. Has this double hash mark right over here is also Other five-centimeter edges because any edge that ![]() So this is one of the five-centimeterĮdges right over here. Could the net below represent the figure? So let's just make sure we understand what this here represents. The net below has five-centimeter and two-centimeter edges. ![]() All the other cases can be calculated with our triangular prism calculator.A figure has a surface area of 40 square centimeters. The only case when we can't calculate triangular prism area is when the area of the triangular base and the length of the prism are given (do you know why? Think about it for a moment). Using law of sines, we can find the two sides of the triangular base:Īrea = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2) Triangular base: given two angles and a side between them (ASA) Using law of cosines, we can find the third triangle side:Īrea = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle) Triangular base: given two sides and the angle between them (SAS) However, we don't always have the three sides given. ![]() area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area).If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base : You can calculate that using trigonometry: Length * Triangular base area given two angles and a side between them (ASA) You can calculate the area of a triangle easily from trigonometry: Length * Triangular base area given two sides and the angle between them (SAS) If you know the lengths of all sides, use the Heron's formula to find the area of the triangular base: ![]() Length * Triangular base area given three sides (SSS) It's this well-known formula mentioned before: Length * Triangular base area given the altitude of the triangle and the side upon which it is dropped Our triangular prism calculator has all of them implemented. A general formula is volume = length * base_area the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. In the triangular prism calculator, you can easily find out the volume of that solid. ![]()
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