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find the area and perimeter of the polygon so let's start with the area first so the area of this polygon there's kind of two parts of this first you have this part that's kind of rectangular or it is rectangular this part right over here and that area is pretty straightforward it's just going to be base times height so area is going to be 8 times 4 8 times 4 for the rectangular part and then we have this triangular part up here so we have this area up here and for a triangle the area's base times height times 1/2 and that actually makes a lot of sense because if you just multiply base times height you would get this entire area you would get the area of that entire rectangle and you see that the triangle is exactly half of it if you took this part of the triangle and you flipped it over you'd fill up that space if you took this part of the triangle and you flipped it over you'd fill up that space so the triangles area is half of the triangles base times the triangles height so plus 1/2 times the triangles base which is 8 inches times the triangles height which is 4 inches and so let's just calculate it this gives us 32 plus plus oh sorry it's not 8 times 4 I want to confuse you it's the triangles height is 3/8 times 3 right there that's the triangles height so once again let's go back and calculate it so this is going to be 32 plus plus 1/2 times 8 is 4 4 times 3 is 12 and so our area for our shape is going to be 44 now let's do the perimeter the perimeter we just have to figure out what's the sum of the size of a fence would we have to build if we wanted to make it around the shape right along the sides of the shape so the perimeter the perimeter I'll just write P for a perimeter it's going to be equal to 8 plus 4 plus 5 Plus this 5 this edge right over here plus I didn't write that down so I have to 5 Plus this 4 right over here so you have 8 plus 4 is 12 12 plus 10 or 12 plus well I'll just go one step at a time 12 plus 5 is 17 17 plus 5 is 22 22 plus 4 is 26 so the perimeter is 26 inches and let me get the unit's right too because over here I'm multiplying 8 set 8 inches by 4 inches so you get square inches 8 inches by 3 inches so you get square inches again so this is going to be square square inches so area is 44 square inches perimeter is 26 inches and that makes sense because this is a two dimensional measurement it's measuring something in two dimensional space so you get a two dimensional unit this is a one dimensional measurement it's only asking you essentially how long would you have what string have to be to go around this thing and so that's why you get one dimensional units