Find the area of the triangle with vertices A(0, 8), O(0, 0), and B(5, 0). What is the area of triangle AOB (in square units)?

Introduction / Context:This question checks coordinate geometry and basic mensuration. When three points are given on the coordinate plane, the area of the triangle can often be found quickly by recognizing a right triangle (two perpendicular sides) or by using the coordinate area formula. Here, two vertices lie on the axes, which strongly suggests a right triangle whose legs are parallel to the x-axis and y-axis. Once we identify the base and height as perpendicular distances along the axes, the area is simply (1/2) * base * height. This is a common aptitude pattern because it avoids heavy computation if you observe the geometry correctly.

Given Data / Assumptions:

• A = (0, 8)
• O = (0, 0)
• B = (5, 0)
• AO is vertical (x = 0), OB is horizontal (y = 0), so AO is perpendicular to OB
• Area of right triangle = (1/2) * base * height

Concept / Approach:Use AO as height and OB as base because they lie on perpendicular axes. Compute their lengths from coordinate differences, then apply the triangle area formula.

Step-by-Step Solution: Length OB = distance from (0, 0) to (5, 0) = 5 units Length AO = distance from (0, 0) to (0, 8) = 8 units Triangle AOB is right-angled at O (axes are perpendicular) Area = (1/2) * OB * AO = (1/2) * 5 * 8 Area = 20 square units

Verification / Alternative check:Using the coordinate triangle area formula also works: Area = (1/2)*|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|. Substituting A(0,8), O(0,0), B(5,0) gives (1/2)*|0*(0-0) + 0*(0-8) + 5*(8-0)| = (1/2)*40 = 20. Same result confirms correctness.

Why Other Options Are Wrong: 8 and 13 can come from confusing side lengths or using (5+8) instead of (1/2)*5*8. 40 is twice the correct value (missing the 1/2 factor). 10 can come from halving only one side incorrectly.

Common Pitfalls:Forgetting the 1/2 in triangle area, misreading coordinates, or not noticing the right angle formed by the axes.

Final Answer:The area of the triangle is 20 sq units.