The area of a compound shape is equal to the sum of the known areas that compound the shape.
In this case, using the dash line as division, we can differentiate a triangle of base b=12 cm and height h=4 cm and a rectangle of sides 4 cm and 12 cm.
Then, the area A of the compound figure is the sum of the area At of the triangle and the area Ar of the rectangle:
[tex]\begin{gathered} A=A_t+A_r \\ A=\frac{b\cdot h}{2}+a\cdot b \\ A=\frac{12\cdot4}{2}+4\cdot12 \\ A=\frac{48}{2}+48 \\ A=24+48 \\ A=72\operatorname{cm}^2 \end{gathered}[/tex]
Answer: the area of the compound shape is 72 cm^2
