![]() ![]() The area of a triangle is one-half times the base times the height. ![]() ![]() So if we find the area of each of these shapes and we add them together, we will have the surface area. So here we’ve drawn the net of the shape. We have the bottom rectangle, and keep in mind that these are not to scale, and then lastly the blue rectangle. So we have these two triangles, which are our bases we have the pink rectangle, found back here and we have this length as 15, because it matches this one. So our hint tells us to draw the net of this shape, which would be all of the faces laying flat so we can easily see them. So if we would like the surface area of this shape, we need to add the area of all of the faces together. That’s what makes up a prism: the two bases and then the rest are rectangles. And it’s a prism because the rest of the faces or the sides is what we can call them are rectangles. The bases, the parallel faces, are triangles. So we have- that this is a triangular prism. ![]() Hint: you can draw the net of the shape to help you. The area of a regular pentagon is found by \(V=(\frac\times2\times1.5)=1.5\), rewrite the equation using this product.Find the surface area of this triangular 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. 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. 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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