To obtain the area(A) of the shaded part of the figure, we will sum up the area of the triangle and the area of the rectangle.
Let us solve the area of the triangle(A1) first,
The formula for the area of the triangle is,
[tex]A_1=\frac{1}{2}\times base\times\text{height}[/tex]
where,
[tex]\begin{gathered} base=b=7 \\ height=a=6 \end{gathered}[/tex]
Therefore,
[tex]A_1=\frac{1}{2}\times7\times6=21unit^2[/tex]
Hence, the area of the triangle is 21 unit².
Let us now solve for the area of the rectangle(A2)
The formula for the area of the rectangle is
[tex]A_2=\text{length}\times width[/tex]
Where,
[tex]\begin{gathered} \text{length}=b=7 \\ \text{width}=c=4 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} A_2=7\times4=28 \\ \therefore A_2=28\text{unit}^2 \end{gathered}[/tex]
Hence, the area of the rectangle is 28unit².
Finally, the total area of the shaded area is
[tex]\begin{gathered} A=A_1+A_2=21+28=49 \\ \therefore A=49unit^2 \end{gathered}[/tex]
Hence, the area of the shaded part is 49unit² (OPTION A).
