Chapter 11.7, Problem 20PSC

To determine

To calculate:Thearea ratio of larger quadrilateral ACEO and smaller quadrilateral BDFH.

Answer to Problem 20PSC

The area ratio is $2:1$ .

Explanation of Solution

Given information:

A quadrilateral BDFH is formed by joining the mid points of sides of quadrilateral ACEO .

Calculation:

  

The below triangles are congruent:

  $\begin{array}{l}△ABH\cong △XBH\\ △GHF\cong △XHF\\ △BCD\cong △XBD\\ △EDF\cong △XDF\end{array}$

So the unshaded portion is congruent to the shaded portion.

  $\frac{A(QuadrilateralACEO)}{A(QuadrilateralBDFH)}=\frac{2}{1}$