Determine the lateral surface area of the given figure.
Now our given figure is a
triangular prism, and our base or cross section is a triangle like this, which is repeated all the
way through the prism. So when we’re asked for the lateral surface area, this means the total area of
all the sides of our prism. So that’s this area plus this area plus this area. So that adds up to
be three different rectangles that make up the sides of our prism.
Now we could work out the area
of each rectangle individually, so 16 times 32, 30 times 32, and 34 times 32, and then add them
together, which gives us a total of 2560. Now each of the individual links were in inches, so the area
is in inches times inches; that’s inches squared or squared inches.
So our answer would be the
lateral surface area is 2560 square inches, but there’s actually a slightly quicker way of doing
the calculation. If I were to slide all of those rectangles together to make one big rectangle, the
length of the longest side would be 16 plus 30 plus 34, which is 80 inches.
So when I work out the
overall area of that rectangle, 80 times 32, I still get 2560 square inches. So if I’d worked out the
perimeter of the base of our prism here and multiplied that by the length of the prism, I get the
same answer, but it takes a bit less working out to do.