The area (Sq.units) of the triangle whose vertices are (3, 8), (−4, 2) and (5, 1) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{61}{2} \)
The area of a triangle with vertices \( (x_{1},y_{1}) \), \( (x_{2},y_{2}) \), \( (x_{3},y_{3}) \) is
\( \displaystyle \frac{1}{2}\left|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})\right| \)
With (3, 8), (−4, 2) and (5, 1):
\( \displaystyle \text{Area}=\frac{1}{2}\left|3(2-1)+(-4)(1-8)+5(8-2)\right| \)
\( \displaystyle =\frac{1}{2}(3+28+30) \)
\( \displaystyle =\frac{61}{2} \)
NCERT (2026-27 edition):
Area of a Triangle
