Explain this question---**Question Stem:**
3. Find the area of the shaded portion of the figure. All angles are right angles. Dimensions are in feet.
**Geometric Figure Description:**
* Type: Geometric figure composed of two nested rectangles.
* Elements:
* An outer rectangle.
* An inner rectangle centered within the outer rectangle.
* The area between the outer and inner rectangles is shaded with diagonal lines.
* Dimensions are labeled:
* The length of the bottom side of the outer rectangle is labeled "7".
* The height of the right side of the outer rectangle is labeled "5".
* The length of the bottom side of the inner rectangle is labeled "5".
* The height of the left side of the inner rectangle is labeled "3".
**Options:**
A. 16 ft²
B. 18 ft²
C. 20 ft²
D. 22 ft²
**Answer:**
**Answer: C. 20 ft²**
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Let's analyze this geometry problem step by step. We have two nested rectangles where the outer rectangle measures 7 feet by 5 feet, and the inner rectangle measures 5 feet by 3 feet. The shaded area is the region between these two rectangles.
First, let's calculate the area of the outer rectangle. The formula for the area of a rectangle is length times width. The outer rectangle has dimensions of 7 feet by 5 feet, so its area is 7 times 5, which equals 35 square feet.
Next, let's calculate the area of the inner rectangle. Using the same formula, area equals length times width. The inner rectangle has dimensions of 5 feet by 3 feet, so its area is 5 times 3, which equals 15 square feet.
Now we can find the shaded area by subtracting the inner rectangle's area from the outer rectangle's area. The shaded area equals 35 square feet minus 15 square feet, which gives us 20 square feet. This matches option C in the multiple choice answers.
Therefore, the correct answer is C, 20 square feet. We solved this by calculating the outer rectangle area of 35 square feet, subtracting the inner rectangle area of 15 square feet, giving us the shaded area of 20 square feet. This systematic approach of finding the difference between two areas is a common method for solving nested rectangle problems.