Graphs

Here's an even easier way to find the area, based on Alan's graph.....

Draw a line segment  connecting  (2,3) and (5,3)

This splits the larger triangle up into two smaller triangles, each with a base of 3 and a height of 2.....thus.....the area of the larger triangle =  2 * (1/2)(3 * 2)   =  6 units^2

One way is to find the length of each side using Pythagoras (length^2 = (ya - yb)^2 + (xa - xb)^2)

Then use Heron's formula:  Area = sqrt(s(s-a)(s-b)(s-c)), where a, b and c are the three side lengths and s is (a+b+c)/2

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use graph paper for this question 

bottom 4 (5-1)

side 2 ( 5-3 ) 

side 4 ( 5-1 ) 

 0.5 x 4 x 2 x 4 = 16 m ^2

Alan's diagram shows an alternative method.

Drop a vertical from the top point (3,5) onto the horizontal through the bottom point (1, 1),

then the area of the triangle is the area of the triangle 'on the left' plus the area of the

parallelogram 'on the right ' minus the area of the triangle ' at the bottom '.