The length of the arc is the length of a segment of the circumference of the circle. The length of the major arc AE is equal to 14.1372 feet.
What is the length of the Arc?
The length of the arc is the length of one of the segments of the circumference of the circle.
[tex]\text{The length of the Arc }= 2\pi r \times \dfrac{\theta}{360^o}[/tex]
As we know the area of the rectangle is 18 sq. st, while the length of one of its sides is 6 ft. Therefore, the length of side AD can be written as,
[tex]\rm \text{Area of the rectangle}=Length \times Breadth[/tex]
Substituting the values for the rectangle ABCD,
[tex]\rm \text{Area of the rectangle}=AB \times AD\\\\18 = 6 \times AD\\\\AD = 3\ feet[/tex]
Thus, the length of the side AD is 3 feet.
As we can see that point D of the circle is at the center of the circle, and line AD is the radius of the circle. We also, know that all the angles of a rectangle are of 90° measure, therefore, the length of the major Arc AE will be 270°(360°-90°).
[tex]\text{The length of the Arc }= 2\pi r \times \dfrac{\theta}{360^o}[/tex]
Substitute the values for the major arc AE,
[tex]\text{ length of the Arc }= 2\pi \times 3 \times \dfrac{270}{360^o}\\\\[/tex]
[tex]\rm = 14.1372\ feet[/tex]
Hence, the length of the major ARc AE is equal to 14.1372 feet.
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