The area of the wall that needs to be painted is the total area, including the door, subtracted by the area of the door. The total area is given by:
![\text{total}=\text{length}\cdot\text{height}](https://img.qammunity.org/2023/formulas/mathematics/college/vpcj65fs4lqleb6kesk1tsbwvtbiuk11ee.png)
Applying the values provided by the problem, we have:
![\text{total}=10\cdot15=150ft^2](https://img.qammunity.org/2023/formulas/mathematics/college/ula5wazaz6nemhd4ukjfsux23lkgqgx5sf.png)
We need to calculate the area of the door now.
![\text{door}=3\cdot7=21ft^2](https://img.qammunity.org/2023/formulas/mathematics/college/hqad5yjqnr67jyqtq8bcqdawv03m7mrd3n.png)
Now we can calculate the area to be painted, the area of the wall.
![\text{wall}=150-21=129ft^2](https://img.qammunity.org/2023/formulas/mathematics/college/uv8ee4v67d175sfsxq5g6npfwk59ipcxv0.png)
Mrs. Johnes need to paint 129 square feet of the wall.