Question

Two figures are arranged as shown. Which of the following can be used to find the area of the figure shaded light gray.

Answer 1

The answer is 9² - x² and x(9 - x) + 9(9 - x)

Explanation:

Here, In a Figure, two square is given first which is small and shaded dark gray and second which is big and shaded light gray.

Now, For area of Small Square.

Length (l) = x

A = l²

A = (x)²

A = x²

Now, For area of Big Square.

Length (l) = 9

A = l²

A = (9)²

A = 81

Then, To find are of Shaded light gray square

Area of Big Square - Area of Small Square.

9² - x²

Thus, The answer is 9² - x² and

x(9 - x) + 9(9 - x)

-TheUnknownScientist

Answer 2

9² − x²

x(9-x)+9(9-x)

Explanation:

The area of the shaded light gray square =

= the area of the whole square - the area of the shaded dark gray square

= 9² - x²

since x(9-x)+9(9-x) = 9x - x² + 9² - 9x = 9² - x²

then x(9-x)+9(9-x) is also a right answer.