Area of shapes on a cartesian coordinate plane

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How to find the area of a shape on a Cartesian coordinate plane.
I welcome to MooMooMath Today we are going to find area of figures on a Cartesian coordinate plane. We will start with some simple figures. If you have a triangle that is graphed and you might have ordered pairs. That is fine if you are given a point like 00 and 5,0 and 2,2. To find the area of the triangle you can use the area formula. 1/2 base times height. On a cartesian coordinate plane you can count the length of the space. It is 5 units long. My height is 2 so I will take I/2 times 5 x 2 =10 and 1/2 of that is 5 squared units.
Lets look at a composite figure. I have a rectangle and a triangle. We can divide it into the two shapes. Take the rectangle first is 2 units long and 2 units high. The area is 4 square units. On top I have a base that measures 2 and my height is one so my area is 1 square unit using the triangle area formula 1/2 base x height
We then add the two areas together because it is a composite figure. We will take 4 + 1 = 5 square units for the area.
Now lets look at some that don't have a height and a base that is vertical or horizontal . What if they are on the Cartesian coordinate plane at a strange angle?
It is a little trickier to find to find the altitude and the height using the distance formula and all kinds of crazy things. There is an easier way to which is the subtraction method. What we will do is label the ordered pairs. We have 0,0, nd we have 9,2 and the ordered pair 3.5 and finally 5,0.
Lets say you have this plotted. You can find the area of the outer rectangle, and then subtract 1 2 3 right triangles and that will give you the area of the shaded region. What is left over. Lets see. The area of the outer shape is 5 by 5 which is 25 square units. You can even count it. You can count up to 25 and see that you have 25 square units. Now we will subtract off these three triangles. This triangle is 3 by 3 Remember the formula for area of a triangle is 1/2 base times height so it is half of 3 x3 which equals 9 and 1/2 of that is 4.5. Now we have another triangle. It is 5 high and 2 units wide 1/2 times 5 x 2 = 10 and which is 4.5
Now the bottom triangle i 5 times 2 and 1/2 base times height gives us 5 square units. Finally we take 25- 10 - 4.5 equals 10.5 square units for the shaded area.

area of shapes | Cartesian coordinate Plane

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