Question

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

Answer 1

Answer:

$9^{2} -x^{2}$

Step-by-step explanation:

The figure is shown in the image attached.

Notice that the shaded light gray area can be calculated by the difference of the bigger square and the smaller square.

The area of the bigger square is: $A_{big}=9^{2}$

The area of the smaller square is: $A_{small}: x^{2}$

The difference between these areas is: $A=9^{2} -x^{2}$

Therefore, the expression that can be used to find the light gray area is: $9^{2} -x^{2}$

Additionally, the expression $x(9-x)+9(9-x)$ is also a right answer, because it's equivalent to the first answer.

$x(9-x)+9(9-x)=9x-x^{2} +81-9x=81-x^{2} =9^{2} -x^{2}$