Answer:
The area of the triangle is 12 unit²
Step-by-step explanation:
The vertices of the triangle are;
a(2, 5), b(5, 9), and c(8, 5)
The area of a triangle given coordinates can be given by the following determinant;
[tex]\Delta = \dfrac{1}{2}\begin{vmatrix}x_1 & y_1 & 1\\ x_2 & y_2 & 1\\ x_3 & y_3 & 1\end{vmatrix} = \dfrac{1}{2} \left | x_{1}\cdot y_{2} - x_{2}\cdot y_{1} + x_{2}\cdot y_{3} - x_{3}\cdot y_{2} + x_{3}\cdot y_{1} - x_{1}\cdot y_{3}\right |[/tex]
Therefore, we have;
[tex]\Delta = \dfrac{1}{2}\begin{vmatrix}2 & 5 & 1\\ 5 & 9 & 1\\ 8 & 5 & 1\end{vmatrix} = \dfrac{1}{2} \left | 2\times 9 - 5\times 5 + 5\times 5 - 8\times 9 + 8\times 5 - 2\times 5 \right |[/tex]
Utilizing an online determinant calculator, we have;
[tex]\dfrac{1}{2} \times \left | -12 \right |= 12[/tex]
Therefore, the area of the triangle is 12 unit².
