 deal with perimeter and circumference so let's take a look at this first one we see the area of a square is 64 square feet and we want to find the squares perimeter well in order to find perimeter we need to know side lengths so let's draw a picture so we have a square and we know that the area is 64 square feet well how do we find area of a square remember area of a square is just one side length raised to the second power and so if we know that the area was 64 we can find one side length by solving that equation so we'll undo that square with a square root and we get that one side length is equal to 8 and so now each of these sides is 8 and so now the perimeter comes pretty quickly remember the perimeter is the sum of all of the sides there are four sides and all the sides of the same so we could just say the perimeter is 4 times 8 in this case that would be 32 feet let's try another problem here we have the area of a circle is 81 pi square feet what is the circles circumference so first off in order to find circumference remember circumference is either pi times diameter or pi times 2 times r so we need either the diameter or the radius so now let's draw a picture we know we have a circle and we know it's area so we have a circle and we know that the area is 81 pi so we'll have to reverse engineer that area remember the area of a circle the formula is pi times r squared and if the area was 81 pi we'll solve the equation 81 pi equals pi times r squared now this looks more complicated than it might be on both sides of the equation we have pi and remember pi is just a number and so that means we can divide both sides of the equation by pi and that leaves us with 81 because pi divided by pi is one pi divided by pi is one so therefore 81 is equal to r squared and now this looks a very similar to the problem that we just solved with the square we want to find the radius so we'll take the square root of 81 and so that gives us a radius of 9 feet now coming back to our circumference we can pick either of these two formulas since I already have the radius I'll use this formula and I know that the circumference is pi times 2 times the radius which was 9 and then we can clean that up 2 times 9 is 18 so we would say that the circumference is 18 pi feet now that would be an exact answer an answer expressed in terms of pi if we wanted to we could multiply 18 times pi or 18 times 3.14 to give an approximate answer but if you're asked for an exact answer you would leave it as 18 pi feet let's try one more minus 3 I believe that's fixed on your on your note sheet so it should be 2x minus 3 now we know the perimeter right the perimeter is given to us is 39 feet so remember to find the perimeter of a triangle the perimeter was side plus side plus side so all three sides added together we have information only about two sides however remember that these congruence marks indicate that if this side is 3x plus 5 then this side is also 3x plus 5 and so now we have all the information about three sides in order to find the length of one of those sides we need to figure out what x is so let's plug this information into our perimeter formula I see that the perimeter that was 39 and that equals one side let's say 3x plus 5 plus another side plus this third side so now we need to solve this equation solve it for x first I see I've got 3x 3x and 2x together that makes 8x then I have plus 5 plus another 5 makes 10 minus 3 and minus 3 plus 7 and that equals 39 now we'll solve that equation we'll subtract 7 from both sides and then divide both sides by 8 so awesome we get that x is equal to 4 but we're not yet done remember let's answer the question that's asked we're asked to find the length of each side so we'll have to substitute x back in so for this side let's say we'd say 3 times 4 plus 5 that'll give us one side length so 12 plus 5 makes 17 I know because these congruence marks that this side is also 17 and then this last side 2x minus 3 so 2 times the quantity 4 minus 3 2 times 4 is 8 minus 3 that gives us a side length of 5 now we see that we were working in feet and so we'll have to go back in and say each of these is 17 feet 17 feet and 5 feet