To find the area of the triangle with vertices at the coordinates \((6, 2)\), \((4, 6)\), and \((1, 2)\), we can use the formula for the area of a triangle given by its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
Assigning the vertices:
- \( (x_1, y_1) = (6, 2) \)
- \( (x_2, y_2) = (4, 6) \)
- \( (x_3, y_3) = (1, 2) \)
Now we can substitute these values into the formula:
\[ \text{Area} = \frac{1}{2} \left| 6(6-2) + 4(2-2) + 1(2-6) \right| \]
Calculating each term inside the absolute value:
- \( 6(6 - 2) = 6 \times 4 = 24 \)
- \( 4(2 - 2) = 4 \times 0 = 0 \)
- \( 1(2 - 6) = 1 \times -4 = -4 \)
Now, add these results together:
\[ 24 + 0 - 4 = 20 \]
Now plug this back into the area formula:
\[ \text{Area} = \frac{1}{2} \left| 20 \right| = \frac{1}{2} \cdot 20 = 10 \]
Therefore, the area of Fiona’s triangle is
\[ \boxed{10} \text{ square units.} \]
1 answer