Question

1. -/1 points find the area of the shaded portion of the figure below given x = 9 ft. ft² resources watch it ebook

Explanation:

Step1: Find side - length of outer square

The side - length of the outer square is $s_{outer}=2x$. Given $x = 9$ ft, then $s_{outer}=2\times9=18$ ft.

Step2: Calculate area of outer square

The area of a square is $A = s^{2}$. So, $A_{outer}=s_{outer}^{2}=18^{2}=324$ $ft^{2}$.

Step3: Find side - length of inner square

The inner square is formed by connecting the mid - points of the sides of the outer square. The side - length of the inner square $s_{inner}=\sqrt{x^{2}+x^{2}}=\sqrt{2x^{2}}=\sqrt{2}x$. Substituting $x = 9$ ft, $s_{inner}=9\sqrt{2}$ ft.

Step4: Calculate area of inner square

Using the formula $A = s^{2}$, $A_{inner}=s_{inner}^{2}=(9\sqrt{2})^{2}=162$ $ft^{2}$.

Step5: Find area of shaded region

The area of the shaded region $A = A_{inner}$. So the area of the shaded region is $162$ $ft^{2}$.

Answer:

$162$