The identical rectangles of dimensions 12 cm x10 cm are overlapping. The over lapped part is a square of side 2 cm. Find the area of it.

The correct answer is: Area of the given figure is 236 cm2.

Hint:-
i. Area of a square = side2
ii. Area of a rectangle = length × breadth
Step-by-step solution:-
From the given information-
length = 12 cm
breadth = 10 cm
side = 2 cm
We know that-
Area of the given identical rectangles = length × breadth
∴ Area of the given identical rectangles = 12 × 10
∴ Area of the given identical rectangles = 120 cm2 ........................................................................ (Equation i)
Area of the given square = side2
∴ Area of the given square = 22
∴ Area of the given square = 4 cm2 .............................................................................................. (Equation ii)
Now, to find the area of the entire figure, we can add the areas of the 2 rectangles.
However, we observe that the overlapping part i.e. the square are is included in areas of both the rectangles.
Hence, we subtract the area of square once to nullify the effect of duplication.
∴ Area of the given figure = 2 (Area of rectangle) - Area of square
∴ Area of the given figure = 2 (120) - 4 ........................................................................................ (From Equation i & ii)
∴ Area of the given figure = 240 - 4
∴ Area of the given figure = 236 cm2
Final Answer:-
∴ Area of the given figure is 236 cm2.
Note:-
The question is not clear on area of which shape is to be found. With the kind of information provided, we assume that area of the entire figure is to be found.