SOLUTION: The radius of the semi-circle centre O is 5cm. A square is fitted into the semi-circle as shown in the diagram. Calculate the area of the square

Question 1177700: The radius of the semi-circle centre O is 5cm. A square is fitted into the semi-circle as shown in the diagram. Calculate the area of the square
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

.
refer drawing , the side of the square on the diameter is symmetric from the centre,
sides of square are 2x each, The diagonal is the radius, = 5 cm. It is a right triangle.
x^2+(2x)^2=5^2=25 ( Pythagoras theorem)

5x^2=25
x^2=5
x= sqrt(5) cm.
2x= 2sqrt(5) cm.
The area of the square is

RELATED QUESTIONS
The radius of a semi circle is 5 cm.A square is fitted inside the semi circle .Calculate... (answered by Fombitz,Boreal)

A square is inscribed in a semi circle having a radius of 15m. The base of the square is (answered by Edwin McCravy)

A quadrilateral ABCD is inscribed in a points semi-circle with side AD as its diameter.... (answered by greenestamps,Edwin McCravy)

A chord of a circle is 24cm long.If the chord is 5cm from th centre of the... (answered by ankor@dixie-net.com,josmiceli)

A chord of a circle is 9cm long. if it's distance from the centre of the circle is... (answered by math_tutor2020,ankor@dixie-net.com)

a triangle of largest size is inscribed in a Semi-circle. if the area of the triangle is (answered by josgarithmetic)

a regular pentagon ABCDE is inscribe in a circle, centre O. calculate angle ABD. well... (answered by greenestamps)

If a wire is bent into the shape of a square, then the area enclosed by the square is 81... (answered by josmiceli)

A side of an equilateral triangle is the diameter of a semi-circle. If the radius of the... (answered by ikleyn)