11 square units
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Explanation:
Refer to the diagram below. I've added point labels A,B,C to the corners of the rectangle. A in the upper left corner, B in the upper right, C in the lower right.
The area of the rectangle is
length*width = AB*BC = 6*4 = 24 square units.
We'll use this value later, so let m = 24
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The area of triangle IAK is
base*height/2 = KA*AI/2 = 2*4/2 = 8/2 = 4 square units
We'll use this value later, so let n = 4
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Repeat the idea of the last section, but do so for triangle KBJ
area = base*height/2
area = JB*BK/2
area = 3*4/2
area = 12/2
area = 6
Triangle KBJ is 6 square units. Let p = 6 so we can use it later.
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Lastly, triangle JCI has area of...
area = base*height/2
area = IC*JC/2
area = 6*1/2
area = 3
Let q = 3
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To summarize everything so far, we have
m = 24 = area of entire rectanglen = 4 = area of triangle IAKp = 6 = area of triangle KBJq = 3 = area of triangle JCI
As you can probably guess where this is going, we'll subtract off the areas of the smaller triangles (n, p and q) from the overall larger rectangle (m) to get the area of triangle IJK.
m - n - p - q = 24 - 4 - 6 - 3 = 11
Triangle IJK has an area of 11 square units.
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An alternative method involves using this outline
Use the distance formula to find the side lengths IK, IJ, and KJThen use Heron's Formula to find the area of the triangle.
