ABCD is a rectangle where AB = 12 cm and BC = 9 cm. E is a point on CD such that DE = 4 cm and EC = 8 cm. Find the area of triangle ABE.
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Worked Solution
Step 1: Identify the correct base and height of triangle ABE.
Vertices: A (bottom-left), B (bottom-right), E (on top side CD).
Choose AB as the base: AB = 12 cm.
Step 2: Find the perpendicular height from E to base AB.
ABCD is a rectangle, so CD is parallel to AB.
The perpendicular distance from any point on CD to AB equals BC = 9 cm.
Height = 9 cm.
Step 3: Calculate the area.
Area = ½ × base × height = ½ × 12 × 9 = 54 cm²
Correct answer: 54 cm²
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