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### Course: Geometry (all content)>Unit 7

Lesson 7: Area of trapezoids & composite figures

# Perimeter & area of composite shapes

Sal finds perimeter and area of a non-standard polygon. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I need to find the surface area of a pentagonal prism, but I do not know how. Can someone tell me?
• For any three dimensional figure you can find surface area by adding up the area of each face. A pentagonal prism 7 faces: it has 5 rectangles on the sides and 2 pentagons on the top and bottom.

It is simple to find the area of the 5 rectangles, but the 2 pentagons are a little unusual. I don't know what lenghts you are given, but in general I would try to break up the unusual polygon into triangles (or rectangles). If I am able to draw the triangles so that I know all of the bases and heights, I can find each area and add them all together to find the total area of the polygon.

This method will work here if you are given (or can find) the lengths for each side as well as the length from the midpoint of each side to the center of the pentagon. Without seeing what lengths you are given, I can't be more specific. Depending on the problem, you may need to use the pythagorean theorem and/or angles.
• would finding out the area of the triangle be the same if you looked at it from another side?
• This is a 2D picture, turn it 90 deg. in either direction, you just see a line going up and down, turn it 45 deg. you have the same picture, just narrower, so no. But if it was a 3D object that rotated around the line of symmetry, then yes.
• Why do you use 8 when multiplying it with the 3 to find the area of the triangle part instead of using 4?
• As he says at , for a triangle the formula is base times height times 1/2. The base of this triangle is 8, and the height is 3.
• How did you get the 3 inches?
(1 vote)
• Area of polygon in the pratice it harder than this can someone show way to do it? thank
• It's pretty much the same, you just find the triangles, rectangles and squares in the polygon and find the area of them and add them all up.
• i dnt understand....Why do you use 8 when multiplying it with the 3 to find the area of the triangle part instead of using 4?
• Sal messed up the number and was fixing it to 3. You'll notice the hight of the triangle in the video is 3, so thats where he gets that number.
• what is a perimeter ? and i need it in mathematical words
• Perimeter is defined as the distance around the outside of a geometrical shape.
• What exactly is a polygon?
• A polygon is a closed figure made up of straight lines that do not overlap. If a shape has a curve in it, it is not a polygon. All the lines in a polygon need to be straight.
• So The Parts That Are Parallel Are The Bases That You Would Add Right?
• to find the area of a shape like this you do height times base one plus base two then you half it
• hi
For school i have to make a shape with the perimeter of 50
i have tried and tried and always got one less 49 or 1 after 51
• Try making a triangle with two of the sides being 17 and the third being 16.
Try making a pentagon with each side equal to 10.
Try making a decagon (pretty hard!) with each side equal to 5.
Hope this helped!

## Video transcript

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.