Questions: In the figure shown, ABCD is a square, with each side of length 8 feet. The width of the border (shaded portion) between the outer square EFGH and ABCD is 3 feet. Find the area of the border

Solution Steps

To find the area of the border, we first need to determine the side length of the outer square EFGH. Since the border width is 3 feet, the side length of EFGH is the side length of ABCD plus twice the border width. Then, calculate the area of both squares and subtract the area of the inner square ABCD from the area of the outer square EFGH to find the area of the border.

The side length of the inner square \(ABCD\) is given as 8 feet. The border width is 3 feet. Therefore, the side length of the outer square \(EFGH\) is calculated as follows:

\[ \text{Side length of } EFGH = 8 + 2 \times 3 = 14 \text{ feet} \]

The area of the inner square \(ABCD\) is calculated using the formula for the area of a square, \(s^2\), where \(s\) is the side length:

\[ \text{Area of } ABCD = 8^2 = 64 \text{ square feet} \]

Similarly, the area of the outer square \(EFGH\) is:

\[ \text{Area of } EFGH = 14^2 = 196 \text{ square feet} \]

The area of the border is the difference between the area of the outer square and the area of the inner square:

\[ \text{Area of the border} = 196 - 64 = 132 \text{ square feet} \]

Final Answer