If the base of a prism is within the shape of an irregular polygon, then the prism is called an irregular prism.īased on the shape of the bases, it is further categorized into different types, namely If the base of a prism is in the shape of a regular polygon, it is called a regular prism. For instance, a square pyramid is cut by a plane, parallel to the base, then the shape of the cross-section of the pyramid will also be a square.ĭepending upon the cross-sections, the prisms are named.
If a prism is intersected by a plane, parallel to the base, then the shape of the cross-section will be the same as the base. It is also said as cutting a three-dimensional object with a plane to get another shape. The cross-section is the point where the shape obtained by the intersection of an object by a plane along its axis. So, a prism can also have a square, a rectangular, a pentagonal, and many other polygon shapes but not a circular shape. The shape of a prism doesn't have any curve. The cross-section looks like a triangle hence called triangular prisms. The area of a regular pentagon is found by \(V=(\frac\times2\times1.5)=1.5\), rewrite the equation using this product.A prism features a very solid shape that consists of two identical ends (like triangle, square, rectangle, etc.), the flat faces or the surfaces, and the uniform cross-section across its length. 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.
#Surface area of a hexagonal prism formula how to#
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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