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In this video you will learn how to find the surface area of a cube, a rectangular prism, a triangular prism, and a square pyramid.
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In this video you will learn how to find the surface area of a cube, a rectangular prism, a triangular prism, and a square pyramid. Let's get started
The formula for finding the area of a cube is 6 times the side squared.
Remember a cube has length sides of the same length, and the length is 10, so 6 times 10 squared equals 6 x 100 which equals 600 meters squared.
Again the formula is 6 times the side squared
With a rectangular prism once you know the formula you just plug in numbers.
The formula will be 2 times length times width
2 times length times height plus 2 times width times the height
Let's identify each of these.
7 will be the length, 3 will be the width, and 4 will be the height
We now just plug in numbers
For the length we have 7 x 3 x 2
Next we have 7 times the height = 7 x 4 x 2
Finally we have the width times the height which is 3 x 4 x 2 and this will equal 42 x 7 x 3 = 21 x 2 = 42 , this is equal to 56 7 x 4 = 28 x 2 = 56 and 3 x 4 = 12 x 2 = 24 add all this up ad it equals 122 and the units will be feet squared.
Let's look at this triangular prism
The formula will be and a triangular pyramid is a little tricky because a slightly different formula.
The formula you will use is is the perimeter of the base and I have shaded it in so you can see it times the height of the prism which equals the lateral area and add that to the area of the two bases of the triangle which equals 2 x 1/2 base times height.
Let's first look at the perimeter equals 3 + 4 + 5 this leg is 5
3 + 4 + 5 times the height, and the way it is sitting the height will be right here so it equals 5 and if you all this together it equals 12 x 5 = 60
Now we have the lateral area. Now we will calculate the area of the two triangular bases. If yo draw this the triangle will look like this and this side is 4 this side is 3 and the hypotenuse is 5 this makes it easier to see.
You will go 1/2 times the base which is 3 x the height which is 4 because it is perpendicular equals 3 x 4 and half of that is 6 and you have 2 of those and that will equal 12 and add those two together equals 72 and your unit of measure is cm squared.
Finally, let's look at the area of this square pyramid
The formula we will use is to calculate the lateral area and add this to the base area.
For the lateral area we will take 1/2 the perimeter times the slant height or slant length.
Since this is a square base we can use side squared.
Let's first look at the perimeter.
he perimeter will be 4 + 4 + 4 + which we can write as 4 x 4 and the slant height is given and it is 6 and 4 x 4 = 16 and 16 and if we take 1/2 x 16 = 8 and 8 x 6 = 48 and that gives us our lateral area. Now we find the base area and we have a side of 4 = 4 x 4 = 16 and that is our base area. Finally we add these together 48 + 16 = 64 inches squared, because surface area is always squared.
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Tagged under: surface area,area,geometry,geometric shapes,cube,rectangular prism,triangular prism,surface area pyramid,math
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