Question

Which of the following statements is true about the figures given below?

• A. The shaded area of Shape $1$ is greater than the shaded area of Shape $2$.
• B. The shaded area of Shape $2$ is approximately equal to the shaded area of Shape $1$.
• C. The shaded area of Shape $1$ is equal to the shaded area of Shape $2$.
• D. The shaded area of Shape $2$ is greater than the shaded area of Shape $1$.

Answer 1

The correct option is C The shaded area of Shape $1$ is equal to the shaded area of Shape $2$.


Shape 1
$AG=AB-BG=CD-BG=6-4=2$ cm ($\because AB=CD$)
Similarly, $AF=AD-FD=BC-FD=9-7=2$ cm ($\because AD=BC$)
Thus, $AF=GE=EF=AG=2$ cm
Thus, $AGEF$ is a square.
Area of a square $=Sid{e}^2$
Area of square $AGEF=2\times 2=4$ sq cm
Area of rectangle $ABCD=Length\times Width=9\times 6=54$ sq cm [$\because Length=9cm,width=6cm$]
Area of Shape $1=$ Area of rectangle $ABCD-$ Area of square $AGEF=54-4$
$=50$ sq cm

Shape 2
Each side of the non-shaded region has a side of length $2$ cm. Thus, it is a square.
Area of the shaded area of Shape $2=$ Area of the red-shaded rectangle $-$ Area of the square of side $2$ cm
$=9\times 6-2\times 2$
$=54-4$
$=50$ sq cm
∴ Area of the shaded area of Shape $1=$ Area of the shaded area of Shape $2$
Thus, option D is the answer.