The area of square LMNP is 50
What is a circle?
A circle is the locus of points equidistant from a fixed point which is known as the center of the circle.
A circle is defined if the center and the radius is known.
Analysis:
Perimeter of a circle = 2πr
Given perimeter = 10π
2πr = 10π
2r = 10
r = 10/2 = 5
r = MO
so the diagonal of the square is actually the diameter of the circle = 5+5 = 10
To find the side, x of the square the diagonal and the sides form a right-angled triangle, by Pythagoras, [tex]10^{2}[/tex] = [tex]x^{2}[/tex] + [tex]x^{2}[/tex]
2[tex]x^{2}[/tex] = 100
[tex]x^{2}[/tex] = 100/2 = 50
Also area of square is [tex]x^{2}[/tex] = 50
In conclusion, the area of square LMNP is 50
Learn more about circles: brainly.com/question/24375372
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