Question

What is the Area of this Triangle? Do not round (A=4,5 B=1,2 C=6,2

Answer 1

To find the area of the triangle given the vertices A(4, 5), B(1, 2), and C(6, 2), we can use the formula for the area of a triangle based on its vertex coordinates:

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

Substituting the coordinates of points A, B, and C into the formula:
- \(A(x_1, y_1) = (4, 5)\)
- \(B(x_2, y_2) = (1, 2)\)
- \(C(x_3, y_3) = (6, 2)\)

Plugging in the values:

\[
\text{Area} = \frac{1}{2} \left| 4(2 - 2) + 1(2 - 5) + 6(5 - 2) \right|
\]
\[
= \frac{1}{2} \left| 4(0) + 1(-3) + 6(3) \right|
\]
\[
= \frac{1}{2} \left| 0 - 3 + 18 \right|
\]
\[
= \frac{1}{2} \left| 15 \right|
\]
\[
= \frac{15}{2}
\]

Thus, the area of the triangle is \(\frac{15}{2}\) or \(7.5\) square units.