SOLUTION: the area of square PQRS is 100 ft ^2 and A,B, C and D are the midpoints of the sides. Find the area of square ABCD.

Algebra ->  Pythagorean-theorem -> SOLUTION: the area of square PQRS is 100 ft ^2 and A,B, C and D are the midpoints of the sides. Find the area of square ABCD.      Log On


   

Question 516386: the area of square PQRS is 100 ft ^2 and A,B, C and D are the midpoints of the sides. Find the area of square ABCD.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Each side length of PQRS is 10. If you draw the midpoints and the segments AB, BC, CD, and DA, you can find the length of each of these statements by noting that you have 45-45-90 triangles. The leg of each triangle is 5, so each of AB, BC, CD, DA is 5sqrt(2). The area of ABCD is (5sqrt(2))^2 = 50 (half the area of ABCD).