Question

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

A. 2.7 or B. 7.5 pick a or b

Answer 1

To find the area of the triangle with vertices at points A(4, 5), B(1, 2), and C(6, 2), we can use the formula for the area of a triangle given by coordinates:

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

Where \((x_1, y_1)\), \((x_2, y_2)\), \((x_3, y_3)\) are the coordinates of points A, B, and C respectively.

Assigning the points:
- A(4, 5) → \(x_1 = 4\), \(y_1 = 5\)
- B(1, 2) → \(x_2 = 1\), \(y_2 = 2\)
- C(6, 2) → \(x_3 = 6\), \(y_3 = 2\)

Plugging these values into the area formula:

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

Calculating each term step-by-step:

1. \(4(2 - 2) = 4(0) = 0\)
2. \(1(2 - 5) = 1(-3) = -3\)
3. \(6(5 - 2) = 6(3) = 18\)

Now combine them:

\[
\text{Area} = \frac{1}{2} \left| 0 - 3 + 18 \right| = \frac{1}{2} \left| 15 \right| = \frac{15}{2} = 7.5
\]

Thus, the area of the triangle is \(7.5\).

**Answer: B. 7.5**