Let us divide the composite figure into two shapes: parallelogram and trapezoid. The sum of the area of both shapes will give the total area of the composite shape.
Area of the parallelogram:
The area of a parallelogram, A₁, is given by
[tex]A_1=b\times h[/tex]
The area is thus calculated as
[tex]\begin{gathered} A_1=3\times4 \\ =12cm^2 \end{gathered}[/tex]
The area of the parallelogram is equal to 12 cm²
Area of the trapezoid:
The area of a trapezoid, A₂, is given by
[tex]A_2=(\frac{a+b}{2})\times h[/tex]
The area is thus calculated as
[tex]\begin{gathered} A_2=(\frac{3+5}{2})\times3 \\ =\frac{8}{2}\times3 \\ =4\times3 \\ =12cm^2 \end{gathered}[/tex]
The area of the trapezoid is equal to 12 cm²
Total Area of Composite Figure
The total area, A, is given as
[tex]\begin{gathered} A=A_1+A_2 \\ =12+12 \\ A=24\operatorname{cm} \end{gathered}[/tex]
The area of the shape is 24 cm².
The correct option is OPTION C.
