Q&A for How to Find Surface Area of a Triangular Prism

A triangular prism is just a box with triangles for the top and bottom. The walls of the box are the same as they are for any other box - rectangular. To find the surface area of the entire prism, you just find the surface area of the top, the bottom, and each wall - then you add them all together. So focus on each step on its own, as if it were its own problem, and write down the answer. What is the surface area of the triangular top? (Write that down.) What is the surface area of the triangular bottom? (Write that down.) Do the same for each wall, then add them all together. Then you're done! You'll find shortcuts along the way, but if they're confusing you now, don't worry about them.

It is not possible to find the surface area of a prism without knowing the height of the prism. If you are given the volume of the prism, it might be possible to derive the height from the formula V = bh, where V equals the volume, b equals the area of the base, and h equals the height. If you know the volume and the area of the base, you can solve for h. From here you can go on to calculate the surface area using the steps above.

2B refers to the total area of the two triangular bases. As with any triangle, calculate the area of either triangular base by multiplying the "base" of the triangle (the length of one of its sides) by its height (the perpendicular distance from that side to the opposite vertex) and then dividing by 2. That gives you the area of either triangular base (B) of the prism. Multiply by 2 to get 2B, the total area of the two triangular bases. To that area you then add the "lateral" area (L) of the prism to get the total surface area (L + 2B).

The only difference is that while a triangular prism has a base consisting of any triangle, a right triangular prism has a base consisting specifically of a right triangle. In either case the volumes are calculated the same way, as are the surface areas.

"Prism" as used here implies a "right prism." Thus, a triangular prism has two bases, each consisting of a triangle, each congruent with the other, and each perpendicular to the planes of the prism's sides.

There's no such thing in relation to a circle. A circle merely has an "area," calculated by πr², where r is the radius.

You would have to know how they are pasted together. Are they pasted together along a lateral side, or along a base? You should calculate the surface area of each prism separately, using the steps above. Then, combine their surface area. Finally, subtract the area of the sides or bases that are pasted together.

For any triangular or rectilinear prism, if each dimension is doubled, the surface area increases by a factor of four, and the volume increases by a factor of eight.

By the Pythagorean theorem, the square of the diagonal minus the square of one side equals the square of the other side. Thus, 26² - 24² = 676 - 576 = 100 = 10², so that the other side measures 10 m, which means the plot's area is 24 x 10 = 240 square meters.

Calculate the volume in whatever units you're given, then use the appropriate conversion factor to convert to liters.

As with any triangle, you have to know the length of one side and the altitude (height) from that side to the opposite vertex. The formula is one-half the length of the side multiplied by the height.

The formula for the lateral surface area is L = Ph. Divide both sides of the equation by P to get L/P = h. Substitute L and P to find h = L/P = 2040/30 = 68cm.

For similar solids, if the ratio of their linear dimensions is a:b, the ratio of their surface areas is (a:b)² = a²:b². Therefore, given that the surface areas of two similar triangular prisms are S1 and S2, calculate the ratio of the areas, S1:S2, by first reducing the ratio (if possible) by dividing S1:S2 by the largest common divisor. Let's say that results in the ratio A:B. Then the ratio of the heights (what you're looking for) is the square root of (A:B) = square root (A) : square root (B). For example, if the surface areas are S1 = 3000 and S2 = 1080, the ratio of the two surface areas is 3000:1080 or 25:9. The ratio of the heights is the square root of (25:9) = √ 25 : √ 9 = 5:3.