Question

Find the area of the following shape. You must show all work to receive credit.

Answer 1

@mathstudent55 this is the last one i need help with

Answer 2

This question was asked earlier today.
I answered it in another post.

Answer 3

http://openstudy.com/users/mathstudent55#/updates/56c9fc3ee4b0641be83b26a8

Answer 4

See that post, but only look at my responses.
The other responses contain errors.

Answer 5

Ohhh okay. I caught up. Could you do a quick summary of a method you use to get 51.5? Because of all that was written on the post, i wanna make sure i completely understand

Answer 6

@mathstudent55

Answer 7

@563blackghost Math student went offline, can you try to summarize what he was trying to say so I can understand better please?

Answer 8

I feel bad asking but its just this is the last question and I wanna turn it in already

Answer 9

i cant really see the explanation cause each time I click on the link and go to his answered questions it always closes it...sorry :(

Answer 10

That's alright, thanks for trying though! Should I just copy and paste what he said?

Answer 11

Actually, instead of summarizing what he said, do you have your own explanation of how to solve this?

Answer 12

If not then I completely understand, after all it confuses me too haha

Answer 13

Ahh ok

Answer 14

The way to answer this question is by having a few things in mind.
1. To find the distance between any two points on the coordinate plane, you are correct that you CAN always use the distance formula, but you DON'T ALWAYS have to use it.
If the two points lie on the same vertical lines, just find the difference in the y-coordinates. Then take the absolute value. If the two points lie on a horizontal line, then find the difference of the x-coordinates, then take the absolute value. This is much easier and quicker than using the distance formula every time. If the graph shows a grid, all you need to do realize the scales used in the grids, and count grid marks to find distances along horizontal and vertical lines.
2. To find the area of a complex polygon like this one, you need to divide it into simple shapes. The shapes don't all have to be triangles. You can use any shape whose area is easy to find. You can use triangles, rectangles, trapezoids, parallelograms, etc. This was the first method I used above.
3. When you calculate the areas of the different shapes, make sure you use the proper dimensions you need. If you calculate the area of a rectangle, make sure you are using a length and a width. If it's a triangle, you need a base and a height. Make sure you know what a base and height are, so you choose the correct dimensions.
4. Sometimes, it's easier to find the area of a larger rectangle outside the entire polygon, and subtract certain shapes. This is what I did in the second method above.

Answer 15

Now subtract from the the area of the large rectangle the ares of the trapezoid P and triangles Q and R.

Trapezoid P: base 1 = 11, base 2 = 6, height = 3
Area = (b1 + b2)h/2 = (11 + 6)(3)/2 = 25.5

Triangle Q: base = 4, height = 3.
Area = bh/2 = 4 * 3/2 = 6

Triangle R: base 5, height = 2
Area = bh/2 = 5 * 2/2 = 5

Area of large rectangle minus areas of P, Q, and R:
88 - 25.5 - 6 - 5 = 51.5

Answer 16

Here is another method he used to get 51.5


: triangle with base 5 and height 3. Area = 5 * 3/2 = 7.5
V: triangle with base 4 and height 3. Area = 4 * 3/2 = 6
W: rectangle with length 3 and width 2. Area = 3 * 2 = 6
X: square with side 5. Area = 5 * 5 = 25
Y: triangle with base 5 and height 2. Area = 5 * 2/2 = 5
Z: rectangle with length 2 and width 1. Area = 2 * 1 = 2
Sum of all areas: --------------------------------> 51.5

Answer 17

U: triangle with base 5 and height 3
V: triangle with base 4 and height 3
W: rectangle with length 3 and width 2
X: square with side 5
Y: triangle with base 5 and height 2
Z: rectangle with length 2 and width 1

~ @mathstudent55

The letters are different shapes so he made a total of 6 different shapes from the irregular shape in which he divided to know shapes....so you would find the areas of these individual shapes...

Answer 18

Once you find the areas of the individual shapes you would then add them up to find the area of the total irregular shape...that is how he got 51.5

Answer 19

Ohhh I get it! I feel so happy for understanding. I thank you both so much for the help!!!

Answer 20

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