Problem Solving

in a XY plane, the coordinates of a triangle ABC are (1,1), (2,6) and (5,4). what is the area of the triangle?
how do i approach to this kinda problem

kinds regards

Nafi

Plot the points and then connect the three dots. One of the best ways in my opinion to come up with the area of the triangle is to enclose a rectangle around it and subtract the area of the 3 different right triangles that you get. In this case, you get the following:

Area of rectangle = 4*5 = 20 units^2

Area of right triangle 1 = (1/2)(2)(3) = 3 units^2

Area of right triangle 2 = (1/2)(5)(1) = 2.5 units^2

Area of right triange 3 = (1/2)(4)(3) = 6 units^2

Therefore the area of the triangle is 20 - (9 + 2.5) = 8.5 units^2

what would be the level of this question??

This problem can be easily solved if we use the vector product rule. We first, find the difference between one point and two other points, and then find the vector product. The whole work is also derived algebraically to avoid matrix manipulations such as S=|(Xâ‚�-X₃)"¢(Yâ‚‚-Y₃)-(Xâ‚‚-X₃)"¢(Yâ‚�-Y₃)|/2 where A(Xâ‚�, Yâ‚�), B(Xâ‚‚, Yâ‚‚) и C(X₃, Y₃) are three different points.

Hence S=|(1-5)*(6-4) - (2-5)*(1-4)|/2 = 17/2 = 8.5

nafiul9090 wrote:in a XY plane, the coordinates of a triangle ABC are (1,1), (2,6) and (5,4). what is the area of the triangle?
how do i approach to this kinda problem

kinds regards

Nafi