Find the area of triangle AFGH with coordinates F(-4,6), G(-2,-1), and H(2,6).

A. 7 square units
B. 21 square units
C. about 21.34 square units
D. 42 square units

Question

High School

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Answer :

nazmalik855 nazmalik855 · Answer 1 · 2023-10-27T18:35:05-04:00

The area of triangle AFGH with coordinates F(-4,6), G(-2,-1), and H(2,6) is approximately 21.34 square units (Option C).

Thus the correct option is C.

To find the area of triangle AFGH, we can use the formula for the area of a triangle given its coordinates. The formula is:

[tex]\[ \text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \][/tex]

In this formula, [tex]\((x_1, y_1), (x_2, y_2),\) and \((x_3, y_3)\)[/tex] are the coordinates of the three vertices of the triangle.

For AFGH, these coordinates are F(-4,6), G(-2,-1), and H(2,6).

Substituting these values into the formula, we get:

[tex]\[ \text{Area} = \frac{1}{2} \left| -4(-1-6) + (-2)(6-(-4)) + (2)((-4)-(-1)) \right| \][/tex]

Solving this expression, we find the area to be approximately 21.34 square units.

Therefore, the correct answer is option C.

The positive value of the area indicates that the vertices are listed in a counterclockwise order, forming a triangle in the coordinate plane.