Question

Use the diagram to determine which statement is true.

Answer 1

Choice C

Area(DEFG) + Area(GHIA) = Area(ABCD)

Explanation:

This is solved using the Pythagorean theorem which states states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides(Wikipedia)

Area of the square on the hypotenuse = Area(ABCD)
Sum of the areas on the other two sides = Area(DEFG) + Area(GHIA)

So we get

Area(ABCD) = Area(DEFG) + Area(GHIA)

which can be re-written as
Area(DEFG) + Area(GHIA) = Area(ABCD)

which is choice C