A trapezoid is formed by cutting a smaller triangle from the top of a larger similar triangle. If the height of the smaller triangle is 1/3 of the height of the larger triangle, what is the ratio of the area of the trapezoid to the area of the larger triangle?
Show answer & explanation
Correct answer: B
Explanation
Given:
Height of the smaller triangle = 1/3 of the height of the larger triangle
By the formula:
Area ratio of areas of similar triangles = (Ratio of sides)²
Small : Sides of the larger triangle = 1 : 3
Area of the smaller : Large triangle = (1/3)² = 1/9
Area of the trapezoid = Area of the larger triangle − Area of the smaller triangle
= 1 − 1/9
= 8/9
Area of the trapezoid : Area of the larger triangle = 8 : 9