Math Problem Statement

In the figure, B is a point lying on AC such that AB : BC = 1 : 2. E is a point on AF such that AE : EF = 3 : 1. It is given that AF || BD and CF || DE. If the area of the trapezium ABDE is 7 cm², then the area of △ACF is?

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Trapezium
Area Ratios
Similarity of Figures

Formulas

Area of trapezium = 1/2 × (sum of parallel sides) × height
Area of triangle = 1/2 × base × height
Ratios of areas of similar triangles = square of the ratio of their corresponding sides

Theorems

Basic Proportionality Theorem (Thales Theorem)
Properties of similar triangles

Suitable Grade Level

Grades 9-12

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