To find the area of the basement you can find the area of the figures that make it up and then add these areas, in other words:
[tex]A_B=A_t+_{}A_s+A_r[/tex]
Where
The formula to find the area of a triangle is
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ Where A is the area}, \\ b\text{ is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]
So, you have
[tex]\begin{gathered} b=6\text{ ft }\Rightarrow\text{ Because 15 ft - 9 ft = 6 ft} \\ h=9\text{ ft} \\ A_t=\frac{b\cdot h}{2}_{} \\ A_t=\frac{6\text{ ft}\cdot9\text{ ft}}{2}_{} \\ A_t=\frac{54ft^2}{2}_{} \\ A_t=27ft^2_{} \end{gathered}[/tex]
The formula to find the area of a square is
[tex]\begin{gathered} A=s^2 \\ \text{ Where A is the area and} \\ s\text{ is one of the sides of the square} \end{gathered}[/tex]
So, you have
[tex]\begin{gathered} s=\text{ 9 ft} \\ A_s=s^2 \\ A_s=(9\text{ ft})^2 \\ A_s=81ft^2 \end{gathered}[/tex]
The formula to find the area of a rectangle is
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where A is the area,} \\ l\text{ is the length and} \\ \text{w is the width of the rectangle} \end{gathered}[/tex]
So, you have
[tex]\begin{gathered} l=15\text{ ft} \\ w=12\text{ ft} \\ A_r=l\cdot w \\ A_r=15\text{ ft}\cdot12\text{ ft} \\ A_r=180ft^2 \end{gathered}[/tex]
Finally, adding the areas you have
[tex]\begin{gathered} A_B=A_t+_{}A_s+A_r \\ A_B=27ft^2_{}+81ft^2+180ft^2 \\ A_B=288ft^2 \end{gathered}[/tex]
Therefore, the area of his basement is 288 square feet.
