hey there it's Kalei and in this lesson we're going to learn to calculate the
surface area of solid figures like cubes and right prisms we've learned how to
find the area of 2d shapes like squares in triangles but now we need to find the
surface area of 3d shapes like cubes and prisms the surface area is the area of
all the faces on a solid figure added together it can be tricky to think about
finding the area of all the faces of a solid object especially when we can't
even see all the faces so here I have a rectangular prism if I want to find the
surface area of this rectangular prism I need to find the area of each face so
let's take the faces apart here I have 1 2 3 4 5 6 so I have 6 different faces
but you notice anything about these faces there's only 3 different shapes
there's 2 of these blue ones 2 of these green faces and 2 of these pink faces so
I would just need to find the area of these faces and then add it all together
to have the surface area of the entire rectangular prism
well we can't take the sides apart like in our last example but we can use a net
to help us visualize our solid figure a net is a drawing that shows the
flattened out version of our figure our cube would have a net that looks like
this we have our square basis here and then our four sides are here remember
this is a cube that means all six sides are congruent squares so to find the
surface area of cube we need to find the sum of the area
of all six squares so now if I know one side length of my square is 2 inches
then I know all of the side lengths are 2 inches so I could find the area of one
square by saying 2 inches times 2 inches which is equal to 4 inches squared so
this is 4 inches squared and since this is a cube I know that each of these
sides and bases are all congruent so their areas are all 4 inches squared so
to find the surface area I would just have to add up all of the areas or find
the sum of all the areas of all 6 sides so I'd have 4 plus 4 plus 4 plus 4 plus
4 plus 4 would give you my surface area or I could say 4 inches squared times 6
because that's the same thing will give me 24 inches squared that's my surface
area nice job so here I have a square prism that means my bases are squares
and it looks like my sides are rectangles so my net will look like this
I have 4 rectangles and 2 squares now if I want to find the surface area I will
need to find the sum of the area of the 2 square bases and add it to the sum of
the area of the four rectangular sides lucky for us we know the formula for
finding the area of squares and rectangles is length times width so if I
know that my squares have a side length of 2 and my rectangles have a side
length of 6 I can find the area of my base would be 2 inches times 2 inches
which is 4 inches squared so that's both of those there and then if I know that
this side here is also equal to 2 inches then the area of my rectangle is equal
to 6 inches times two inches and that gives me 12 inches
squared so that's gonna be the same for all of these so now what what I have to
do I have to add up all of these areas together or I can find the surface area
of my bases is equal to two times four inches squared which is equal to eight
inches squared and the surface area of my sides is equal to four times twelve
inches squared four times twelve that gives me 48 inches squared and now all I
have to do is find the sum of these here so 48 plus eight that gives me 56 inches
squared and that would be the total surface area of my square prism now what
about our triangular prism what would it look like flattened out this triangular
prism would have two triangle bases and three rectangle sides so the surface
area would be the sum of the area of the triangles plus the sum of the area of
the rectangles all right so let's find the area for my base here it's a
triangle so I have base times height base is two inches times my height one
point seven inches divided by two that gives me three point four inches squared
divided by two that's going to be equal to one point seven inches squared so
that's area for this space and one point seven inches squared over here now
what's the area for one of my sides one of these rectangles I have three inches
times two inches three inches times two inches that gives me six inches squared
sum into all of these are six inches squared as well so the surface area of
my bases I have two triangles that each have an area of one point seven inches
squared so that gives me a total of three point
four inches squared and my rectangles give me a
surface area of my sides of three times six inches squared and that is equal to
eighteen point two zero inches squared and if I find my sum here I bring down
my four eight nine ten eleven carry my one two when I bring my decimal point
down inches squared so that's the total surface area for this trained healer
prism great work learning how to use nets to calculate the surface area of
cubes and prisms practice what you've learned by doing the online games and
quizzes have fun and remember to always be clever