Question

In The figure below ABCD is a square points are chosen on each pair of the adjacent sides of ABCD to form four congruent and right angles as shown below each of these has one leg that is twice as long as the other leg what fraction of the area of square ABCD is shaded?​

Answer 1

5/9 of the area is shaded.

Explanation:

Answer 2

9514 1404 393

Answer:

5/9

Explanation:

The area of one triangle is ...

A = 1/2(x)(2x) = x²

Then the area of the four triangles is ...

unshaded area = 4(x²)

The length of DC is 2x+x = 3x, so the area of ABCD is ...

total area = (3x)² = 9x²

Then the fraction that is shaded is ...

(9x² -4x²)/(9x²) = 5/9

5/9 of the area of ABCD is shaded.