Trapezoidal Prism-Surface Area and Volume

In this video I would like to talk about finding the surface area and volume of a trapezoidal prism. The reason this is a trapezoidal prism is because it has two bases that are trapezoids.
The volume formula is 1/2 the height of the trapezoid times base 1 plus base 2 ( trapezoid has base sides of different length) times the height of the prism, and the height is the distance between these two bases.( I will have the height of the prism as a capital H)
Now I will just plug in numbers.

Volume = 1/2 height and remember the height is a perpendicular line to the two bases and this would be a 90 degree and that is 2 times base 1 which is 3.5 plus the second base which is 6 times the height of the prism, which is 4.
Now when I complete the math 3.5 + 6 = 9.5 x 2 = 19 times 1/2 equals 9.5 and multiply that by 4 equals 38 units cubed

Now lets find the surface area is two parts.
First you find the lateral area and by taking the perimeter times the height plus two base areas.
The formula for base area is 1/2 times height of the trapezoid times base 1 plus base 2 times the trapezoidal height
Lets start with the lateral area
First we need t find the perimeter and that is given, will equal 2.5 + 3.5 + 2.5 + 6 and after adding we will multiply this by the height of the prism and it is given and is 4
When we add 2.5 + 3.5 + 2.5 + 6 = 14.5 times 4 which is the prism height equals 58 which is 1/2 our total surface area the lateral area
Next we need to find the area of the bases
Use 1/2 times height of the trapezoid times base 1 plus base 2
Now I will fill in the numbers 1/2 times the height which is given 2 times base 1 which is 3.5 plus base 2 and when I multiply this I get 9.5 times 2 equals 19 divided by 2 = 9.5 but then I have two bases so I will add two of these for the two bases.
9.5 + 9.5 = 19
The area of one base is 9.5, but we have two of those so I will add these together and that equals 19 and now just add lateral area of 58 plus the base areas of 19 and that equals 77 squared
Hope this helps in finding the volume and surface area of a trapezoidal prism
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