Area of trapezoids & composite figures
Perimeter & area of composite shapes
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's going to be 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 is base times height times 1/2. And that actually makes a lot of sense. Because if you just multiplied 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 1/2 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 triangle's area is 1/2 of the triangle's base times the triangle's height. So plus 1/2 times the triangle's base, which is 8 inches, times the triangle's height, which is 4 inches. And so let's just calculate it. This gives us 32 plus-- oh, sorry. That's not 8 times 4. I don't want to confuse you. The triangle's height is 3. 8 times 3, right there. That's the triangle's height. So once again, let's go back and calculate it. So this is going to be 32 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 sides. How long of a fence would we have to build if we wanted to make it around this shape, right along the sides of this shape? So the perimeter-- I'll just write P for 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 two 5's plus this 4 right over here. So you have 8 plus 4 is 12. 12 plus 10-- 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 units right, too. Because over here, I'm multiplying 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 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 a string have to be to go around this thing. And so that's why you get one-dimensional units.