What is the area of this Triangle? Geometry.

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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

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

f

step-by-step explanation:

f

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2