Give an explanation to go with your answer! a rectangle is placed symmetrically inside a square. the rectangle has sides of length m and n. find the area of the square in terms of m and n.

Step-by-step explanation:

Look at the picture.

We have the triangles 45° - 45° - 90°. The sides are in ratio 1 : 1 : √2

(look at the second picture).

Therefore we have the equations:

 and  

Solve:

               multiply both sides by √2

              divide both sides by 2

               multiply both sides by √2

            divide both sides by 2

The side length of square is

The area of a square:

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²