# Thread: Finding the area of the shaded region?

1. ## Finding the area of the shaded region?

Ok I have these three points of the Cartesian plane (0,0),(2,3),(5,0)

And I have to find the area "inside these points" to me they look like a triangle

So I thought I would use 1/2 base(height)

I used the distance formula to get the base from (0,0) to (5,0) as 5

I got height from from (2,3) to (0,0) as 5

So I did (1/2)(5)(5)=12.5 only problem is that the answer in the back of my textbook says 15/2.

2. ## Re: Finding the area of the shaded region?

Originally Posted by homeylova223
Ok I have these three points of the Cartesian plane (0,0),(2,3),(5,0)

And I have to find the area "inside these points" to me they look like a triangle

So I thought I would use 1/2 base(height) perpendicular height for the base you choose

I used the distance formula to get the base from (0,0) to (5,0) as 5

I got height from from (2,3) to (0,0) as 5 this is not the perpendicular height for the chosen base

So I did (1/2)(5)(5)=12.5 only problem is that the answer in the back of my textbook says 15/2.
Note that there is no need to use the distance formula
to get the distance from (0,0) to (5,0)
as these points are both on the horizontal x-axis
so the distance is 5-0=5.

The x and y axes are perpendicular.
Hence you want the distance from (2,3) to (2,0) as the perpendicular height,
which is 3.

Now you can use the area of a triangle = half the base times the height.

3. ## Re: Finding the area of the shaded region?

Originally Posted by homeylova223
I got height from from (2,3) to (0,0) as 5
May be a good idea for you to buy some graph paper...

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### area of shaded region sta

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