a side of an inner Square measures 10 cm and the outer square measures 30 centimeters what is the area of one of the trapezoid tiles

Answer 1

We assume the inner square is completely centered inside the outer square, otherwise the trapezoid tiles would have different areas.

Here is the shortcut:

since the 4 trapezoid tiles are congruent and have equal areas A, and their total area is the difference of the areas of the inner and outer squares. So 30² - 10² = 4A, 900 - 100 = 4A, 800 = 4A, 200 = A.

The longer way is to decompose a trapezoid into a 10 x 10 square, and two right isosceles triangles with side 10. The area A is then 10² + 2 (1/2 * 10 * 10), using the area of a triangle is 1/2 Base * Height. Again, A = 200.