Question : The area of triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:
Option 1: 8 sq. units
Option 2: 13 sq. units
Option 3: 20 sq. units
Option 4: 40 sq. units
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Correct Answer: 20 sq. units
Solution : Let (x 1, y 1 ) = (0, 8) (x 2, y 2 ) = (0, 0) (x 3, y 3 ) = (5, 0) Area of a triangle with vertices (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ) = $\frac{1}{2}$ [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )] = $\frac{1}{2}$ [0(0 – 0) + 0(0 – 8) + 5(8 – 0)] = $\frac{1}{2}$[40] = 20 sq. units Hence, the correct answer is 20 sq. units.
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