SOLUTION: The radius of a semi circle is 5 cm.A square is fitted inside the semi circle .Calculate the area of the square

Question 1029427: The radius of a semi circle is 5 cm.A square is fitted inside the semi circle .Calculate the area of the square
Found 2 solutions by Fombitz, Boreal:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
.
.
.
.
From the diagram,

The area of a square with side, , would be,

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If you draw this, the side of the square on the diameter is symmetric from the center, and let each part be x.
But the sides are now 2x each, so the vertical sides, extending to the semicircle, are 2x. The diagonal is the radius, or 5 cm. That is a right triangle.
x^2+(2x)^2=5^2=25
5x^2=25
x^2=5
x= +sqrt(5) cm.
2x= 2sqrt(5) cm.
The area of the square is twice x or [2(sqrt(5)]^2=4*5=20 cm^2
RELATED QUESTIONS
The radius of the semi-circle centre O is 5cm. A square is fitted into the semi-circle as (answered by mananth)
A side of an equilateral triangle is the diameter of a semi-circle. If the radius of the... (answered by ikleyn)
A square is inscribed inside a quadrant of a circle of radius 10 cm. Calculate the area... (answered by dabanfield)
If a wire is bent into the shape of a square, then the area enclosed by the square is 81... (answered by josmiceli)
A square is inscribed in a semi circle having a radius of 15m. The base of the square is (answered by Edwin McCravy)
A rectangle is inscribed inside the semi-circle y=square root of 100-x^2. what are the... (answered by Fombitz)
a triangle of largest size is inscribed in a Semi-circle. if the area of the triangle is (answered by josgarithmetic)
If the radius of a circle is increased by 30% then the area of the semi circle is... (answered by ccs2011)
A semi circle is attached to a triangle. What is the total area of the shape ,if the... (answered by josgarithmetic)