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Answer :
Final answer:
When the vertices of a triangle are given as coordinates, the area can be calculated by halving the sum of [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]. Applied to the coordinates of triangle KLM, the area is 7 square units.
Explanation:
The area of a triangle when the coordinates of vertices are given can be calculated using the formula 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]. Here, (x1,y1), (x2,y2) and (x3,y3) are the coordinates of the vertices of triangle KLM.
In this case, K(2,3) can be taken as (x1,y1), L(7,4) as (x2,y2) and M(3,6) as (x3,y3). Plugging these values into the formula, we get 1/2[2*(4-6) + 7*(6-3) + 3*(3-4)], which simplifies to 1/2[-4 + 21 - 3], and further simplifies to 7 square units.
Therefore, the area of triangle KLM is 7 square units.
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