![]() Surface area of trapezoidal prism = h (b + d) + l (a + b + c + d) Surface area of rectangular prism = 2(lb + bh + lh) Surface area of square prism = 2a 2 + 4ah ![]() Surface area of triangular prism = bh + (s1 + s2 + b)H Surface Area of Prism = (2 × Base Area) + (Base perimeter × height) See the table below to understand this concept behind the surface area of various prism: Shape ![]() The bases of different types of prisms are different so are the formulas to determine the surface area of the prism. Thus, the lateral surface area of prism = base perimeter × height The total surface area of a Prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height). The lateral area is the area of the vertical faces, in case a prism has its bases facing up and down. Let us look at the surface area of the prism formula The total surface area of a prism is the sum of lateral surface area and area of two flat bases. To find the surface area of any kind of prism we use the general formula. Finding the surface area of a prism means calculating the total space occupied by all the faces of that respective type of prism or the sum of the areas of all faces (or surfaces) in a 3D plane. The area of a regular pentagon is found by \(V=(\frac\times2\times1.5)=1.The surface area of a prism refers to the amount of total space occupied by the flat faces of the prism. This formula isn’t common, so it’s okay if you need to look it up. 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. 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. ![]()
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