1.

The given figure shows a rectangle. Find the area of the shaded region within the rectangle.

Answer» We can provide the points to the given rectangle. Let `ABCD` is the given rectangle.
Please refer to video for the complete figure.
From the figure,
Area of shaded region = Area of rectangle ABCD - (Area of triangle AEF + Area of triangle DEC)
We are given `AE = ED`
Also, `AD = 12` cm
Now, `AE =ED = (AD)/2 = 12/2 = 6` cm
So, Area of `Delta AEF(A_1) = 1/2**b**h`
Here, `b = AE = 6` cm, `h = 7` cm
`=> A_1 = 1/2**6**7 = 21cm^2`
Similarly, Area of `Delta DEC(A_2) = 1/2**6**7 = 21cm^2`
Now, Area of rectangle ` = l*b = 12*7 = 84cm^2`
So, Area of shaded region `= 84-(21+21) = 42cm^2`


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