We want to substitute in our formula for the area of a regular pentagon. Remember, with surface area, we are adding the areas of each face together, so we are only multiplying by two dimensions, which is why we square our units.įind the volume and surface area of this regular pentagonal prism. Remember, since we are multiplying by three dimensions, our units are cubed.Īgain, we are going to substitute in our formula for area of a rectangle, and we are also going to substitute in our formula for perimeter of a rectangle. When we multiply these out, this gives us \(364 m^3\). Since big B stands for area of the base, we are going to substitute in the formula for area of a rectangle, length times width. Examplesįind the volume and surface area of this rectangular prism. Now that we know what the formulas are, let’s look at a few example problems using them. The formula for the surface area of a prism is \(SA=2B+ph\), where B, again, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism. We see this in the formula for the area of a triangle, ½ bh. It is important that you capitalize this B because otherwise it simply means base. Notice that big B stands for area of the base. To find the volume of a prism, multiply the area of the prism’s base times its height. Now that we have gone over some of our key terms, let’s look at our two formulas. Remember, regular in terms of polygons means that each side of the polygon has the same length. The height of a prism is the length of an edge between the two bases.Īnd finally, I want to review the word regular. Height is important to distinguish because it is different than the height used in some of our area formulas. The other word that will come up regularly in our formulas is height. For example, if you have a hexagonal prism, the bases are the two hexagons on either end of the prism. The bases of a prism are the two unique sides that the prism is named for. The first word we need to define is base. Let us solve some examples to understand the concept better.Hi, and welcome to this video on finding the volume and surface area of a prism!īefore we jump into how to find the volume and surface area of a prism, let’s go over a few key terms that we will see in our formulas. Total Surface Area ( TSA) = ( b × h) + ( s 1 + s 2 + s 3) × l, here, s 1, s 2, and s 3are the base edges, h = height, l = length The formula to calculate the TSA of a triangular prism is given below: The total surface area (TSA) of a triangular prism is the sum of the lateral surface area and twice the base area. Lateral Surface Area ( LSA ) = ( s 1 + s 2 + s 3) × l, here, s 1, s 2, and s 3 are the base edges, l = length Total Surface Area The formula to calculate the total and lateral surface area of a triangular prism is given below: The lateral surface area (LSA) of a triangular prism is the sum of the surface area of all its faces except the bases. It is expressed in square units such as m 2, cm 2, mm 2, and in 2. The surface area of a triangular prism is the entire space occupied by its outermost layer (or faces). Like all other polyhedrons, we can calculate the surface area and volume of a triangular prism. So, every lateral face is parallelogram-shaped. Oblique Triangular Prism – Its lateral faces are not perpendicular to its bases.Right Triangular Prism – It has all the lateral faces perpendicular to the bases.
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