The figure is made up of a square and a rectangle. Find the area of the shaded region.

24 m^2.

Step-by-step explanation:

Length of rectangle = 16 m - side of square

                   ⇒  16 m - 7 m

Length of rectangle = 9 m

In rectangle  :

⇒ Area of shaded region

⇒ Area of half rectangle

⇒  ( 3 m x 9 m ) / 2

⇒ 1.5 x 9 m^2

⇒ 13.5 m^2           ...( 1 )

In square,

⇒ Area of square = ( 7 m )^2

⇒ Area of square = 49 m^2

Also,

⇒ Area of total non-shaded region = ( area of triangle formed by diagonal ) + ( area of right-angled triangle of height 7 m and base ( 7m - 3m ) = 4m )

⇒ Area of non-shaded region = ( 7 m x 7 m / 2 ) + ( 7 m x 4 m / 2 )

          ⇒ 24.5 m^2 + 14 m^2

          ⇒ 38.5 m^2

Thus,

⇒ Area of shaded region in square = area of square - area of square region in square  

          ⇒  49 m^2 - 38.5 m^2

          ⇒  10.5 m^2        ...( 2 )

⇒ Area of total shaded region = ( 1 ) + ( 2 ) = area of shaded region in square + rectangle

⇒  13.5 m^2 + 10.5 m^2

⇒  24 m^2

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