Find area of a triangle in coordinate plane

In summary, the conversation discussed finding the area of a rectangle with three right triangles within it. The central triangle was not a right triangle and did not satisfy the Pythagorean Theorem. The bounding rectangle had an area of 20 and the total area of the three right triangles was 13. Subtracting this from the rectangle's area gave the answer of 7.
  • #1
funnijen
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  • #2
Hello, and welcome to MHB! (Wave)

\(\displaystyle \triangle QRS\) is not a right triangle, but I suspect what is intended is for you to find the area of the rectangle, and then subtract away the areas of the 3 right triangles that are within the rectangle, but not part of \(\displaystyle \triangle QRS\).

Can you proceed?
 
  • #3
Um does the position on the grid mean anything. i honestly only know 1/2BH formula and its not giving me the right answer. I honestly don't know any part of how to do this
 
  • #4
I figured it out! 7 is the answer. Thanks!
 
  • #5
Very good! For those who are interested, MarkFL could see that the central triangle was NOT a right triangle because it does not satisfy the "Pythagorean Theorem". The two legs have length 5 and [tex]2\sqrt{2}[/tex] while the hypotenuse has length $\sqrt{29}$. $29\ne 25+ 8$.

The bounding 4 by 5 rectangle has area 20. The right triangle at the upper left corner has area 3(4)/2= 6. The right triangle at the lower left has area 2(2)/2= 2. And the right triangle at the right has area 2(5)/2= 5. Those have total area 6+ 2+ 5=13 so the area of the central triangle is 20- 13= 7 as funnigen said.
 

What is the formula for finding the area of a triangle in the coordinate plane?

The formula for finding the area of a triangle in the coordinate plane is A = 1/2 * base * height, where the base is the length of the triangle's base and the height is the perpendicular distance from the base to the opposite vertex.

How do you find the coordinates of the vertices of a triangle in the coordinate plane?

To find the coordinates of the vertices of a triangle in the coordinate plane, you can use the distance formula or the Pythagorean theorem. You can also use the midpoint formula to find the coordinates of the midpoint of each side, and then use those points to find the coordinates of the vertices.

What is the difference between a right triangle and an oblique triangle?

A right triangle has one angle that measures 90 degrees, while an oblique triangle has no angles that measure 90 degrees. This means that the sides of a right triangle are perpendicular to each other, while the sides of an oblique triangle are not.

Can you find the area of a triangle in the coordinate plane if you only know the coordinates of two vertices?

Yes, you can find the area of a triangle in the coordinate plane if you know the coordinates of two vertices. You can use the distance formula to find the length of the third side, and then use the formula A = 1/2 * base * height to find the area.

Is there a specific order in which the coordinates of the vertices of a triangle in the coordinate plane should be listed?

Yes, the coordinates of the vertices of a triangle in the coordinate plane should be listed in a specific order. This order is known as the "counterclockwise order" and it starts at any vertex and goes around the triangle in a counterclockwise direction. This order is important because it determines the orientation of the triangle and affects the calculation of the area.

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