![]() The area of a regular pentagon is found by \(V=(\frac\times2\times1.5)=1.5\), rewrite the equation using this product. 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. Now that we know what the formulas are, let’s look at a few example problems using them.įind the volume and surface area of this rectangular prism. 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. A triangular prism consists of three inclined rectangular surfaces and two parallel triangle bases. The sum of the lengths of the rectangles is equal to the perimeter of the triangles.Ī cylinder unfolded into a net is made up of two identical circles and a rectangle with a length equal to the circumference of the circles.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. The total surface area of a Prism 2 (Base Area) (Base perimeter × height) square units Triangular Prism A prism with a triangular base is referred to as a triangular prism. CubeĪ cube unfolded into a net is made up of six identical squares.Ī triangular prism unfolded into a net is made up of two triangles and three rectangles. To calculate the surface area we therefore find the area of the two circles and the rectangle and add them together.īelow are examples of right prisms and a cylinder that have been unfolded into nets: Rectangular PrismĪ rectangular prism unfolded into a net is made up of six rectangles. In the case of a cylinder the top and bottom faces are circles and the curved surface flattens into a rectangle with a length that is equal to the circumference of the circular base. To calculate the surface area of the prism, we find the area of each triangle and each rectangle, and add them together. In order to calculate the surface area of the prism, we can then simply calculate the area of each face, and add them all together.įor example, when a triangular prism is unfolded into a net, we can see that it has two faces that are triangles and three faces that are rectangles. When a prism is unfolded into a net, we can clearly see each of its faces. A solid that is unfolded like this is called a net. This is easier to understand if we imagine the prism to be a cardboard box that we can unfold. Surface area is the total area of the exposed or outer surfaces of a prism.
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