ANSWER
Area is 5921.28 m^2
Frank made an error by subtracting the area of the square from the area of the 4 semi-circles.
EXPLANATION
Given:
Desired outcome:
1. Area enclosed by the figure
2. The error made by Frank.
Find the area of the 4 semi-circles
[tex]\begin{gathered} Area\text{ of a semi-circle = }\frac{\pi\text{ r}^2}{2} \\ \text{ = }\frac{3.14\times(24)^2}{2} \\ \text{ = 904.32} \end{gathered}[/tex][tex]\begin{gathered} Area\text{ of 4 semi-circles = 4}\times904.32 \\ \text{ = 3617.28 m}^2 \end{gathered}[/tex]Find the area of the square
[tex]\begin{gathered} Area\text{ of a square = l}^2 \\ \text{ = 48}^2 \\ \text{ = 2304 m}^2 \end{gathered}[/tex]The area enclosed by the figure
The area enclosed by the figure is determined by adding the area of the 4 semi-circles to the area of the square.
[tex]\begin{gathered} Area\text{ enclosed by the figure = Area of the square + area of the 4 semi-circles} \\ \text{ = 2304 + 3617.28} \\ \text{ = 5921.28 m}^2 \end{gathered}[/tex]Error made by Frank
Frank made an error by subtracting the area of the square from the area of the 4 semi-circles
i.e:
[tex]3617.28\text{ - 2304 = 1313.28 m}^2[/tex]Hence, the area enclosed by the figure is 5921.28 m^2 and Frank made an error by subtracting the area of the square from the area of the 4 semi-circles.
