How To: Find the area of a triangle given three points

If the triangle is not a right triangle, how would you find the base and height. For example: point 1: (1, 5), point 2: (3, 6), point 3: (2, 7).

Use two points and create a line. that line will be the base of the triangle. Then with the third point you can join it with the two points of the base to create a triangle. Then with the third point that is not the base, create a perpendicular line to the base. now find the slope of the base. The perpendicular line will have a slope that is the negative reciprocal of the base's slope. use pont slope formula and substitute the values of the slope value ,x value and y value into the formula. I will use capital letters to show the different values. Y-y=m(X-x) . m stands for the value of the slope. You can use the distance formula to find the length of the base. for example, if your given points that make up your base is (0,3) and (4,0) you can use the distance formula to get that the length between the two points is 5. Find the base length. Then find the equation of the base. use the point slope formula mentioned before. the equation of my base can be either Y-3= -3/4 (X-0) or the equation can be Y-0= -3/4 ( X-4) since you can use any points on the base (or the line) to find the equation of the base. You also need to find the slope. you know that the perpendicular line to the base and the base intersect eachother. you set the equation of the base and the perpendicular line to y-intercept form. so my base equation becomes Y=-3/4x+3. for the equation of the perpendicular line, use the third given point. the third given point of my triangle is (0,0) so the equation is Y-0= 4/3 (X-0) so the y intercept form is Y=4/3(x). Set the two equations equal to eachother. So i take -3/4x+3 and 4/3(x) and get 4/3x=-3/4x+3. Solve for X and that will give you the x value for the intersection point. and then find the y value. then use distance formula. I did this really quick so dont trust me so much on the answer. just use method