A triangle has a base of 18 cm and a height of 12 cm. A line is drawn parallel to the base at a distance of one-third of the total height measured from the apex. Find the area of the smaller triangle formed above this line.
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Worked Solution
Step 1: Find the height of the smaller triangle.
The line is drawn at ⅓ of the total height from the apex.
Height of smaller triangle = ⅓ × 12 = 4 cm
Step 2: Find the base of the smaller triangle using similar triangles.
The smaller triangle is similar to the original triangle with scale factor = ⅓ (same as the height ratio).
Base of smaller triangle = ⅓ × 18 = 6 cm
Step 3: Find the area of the smaller triangle.
Area = ½ × 6 × 4 = 12 cm²
Correct answer: 12 cm²
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