l = 8 in
w = 3 in
h = 5 in
Given our variables we can find the area of each face/side of the rectangular prism.
We can find the top and bottom faces of our rectangular prism by using the following formula:
A1 = 2 (l × w)
The 'l' represents the length, and the 'w' represents the width of the rectangular prism. 'A' represents the area, and the '2' means we double that area because there are two faces with the same area: top and bottom.
Now we can substitute the 'l' and the 'w:'
A1 = 2 (8 × 3)
= 2 (24)
= 48 in^2
Now that we know the overall area of the top and bottom faces of the rectangular prism we can find the two side faces:
A2 = 2 (l × h)
Again, 'l' means the length of the rectangular prism while 'h' means the height. The '2' represents the two sides and means that we need to times the (l × h) by two. We can now substitute our values:
A2 = 2 (8 × 5)
= 2 (40)
= 80 in^2
So, the two side faces have a total of 80 in^2. We can now find the front and back sides using the following formula:
A3 = 2 (w × h)
We substitute the known values:
A3 = 2 (3 × 5)
= 2 (15)
= 30 in^2
Now we know the total area of the top and bottom faces, the total area of the side faces, and the total area of the front and back faces. To find the 'total surface area' (TSA) that Ramona will paint, we add our three results:
TSA = A1 + A2 + A3
= 48 + 80 + 30
= 158 in^2
The 'total surface area' that Ramona will paint is 158 in^2.
NOTE: The in^2 means 'inches squared' and is a unit of measurement applied to when finding the area of an object or thing in inches.
THE FORMULA:
The formula to find the 'total surface area' of a rectangular prism is given by:
TSA = 2(lw + lh + wh)
When the length, l, width, w, and the height, h, are given, just substitute the values into the formula.
