Question

In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Which of the following is true.

• A. area (ABCDE) = area(ABCF)
• B. area (AEDF) = area (ABCDE)
• C. area (AEDF) = area (ABCF)
• D. area (DEAF) = area (ABCF)

Answer 1

The correct option is B

area (AEDF) = area (ABCDE)

$△$ACB and $△$ACF lie on the same base AC and are between the same parallels AC and BF.

$\therefore$ Area ($△$ACB) = Area ($△$ACF)

$\Rightarrow$ Area ($△$ACB) + Area (ACDE) = Area ($△$ACF) + Area (ACDE)

$\Rightarrow$ Area (ABCDE) = Area (AEDF)