– English Lyrics

Lyrics & Translation

[English]

today we have to find the area of this

inscribed Square only given thing is

this radius of the quarter Circle which

is 10 can you solve it let us label the

side of this Square as X if you see this

line of the square it also represents

the chord of the quarter Circle so we

can use a perpendicular bis sector which

will divide this chord into two equal

parts therefore this piece will be x/2

this piece is the same as the side of

the square that is X now consider this

right triangle since both of these lines

are parallel therefore this

perpendicular bis sector will also

divide this side into two equal parts

and thus both of these angles will also

be the same which will be

45° so this will be an isoceles right

triangle which means all of these angles

will be

45° now consider this part both angles

are equal therefore this side will also

be = to x / 2 all right now we will

construct a line from the center of this

quarter Circle to this vertex of the

square this line is also the radius of

the circle and thus it will be 10 great

now finally consider this right triangle

this side is X /2 this side will be x /

2 + x or 3 x / 2 and the hypotenuse is

10 so using Pythagoras Theorem we get 10

2 = x / 2 2 + 3 x / 2 2 this will be x²

over 4 + this will be 9 x² over 4 and it

will be equal to 100 this will become 1

+ 9 or 10 x^2 / 4 = 100 so 10 x² will be

400 or x² = 40 our question was to find

the area of this inscribed square and

since its side is X therefore the area

will be x square or 40 this is our

answer don't forget to put the square

units so good