Question

what is the area of the wall that will be painted green?

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 12\) ft and \(w=(6 + 3)=9\) ft. So, \(A_{rectangle}=12\times9 = 108\) square feet.

Step2: Calculate the area of the non - green triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\).
For the upper triangle: \(b = 12\) ft, \(h = 6\) ft. So, \(A_{upper}=\frac{1}{2}\times12\times6=36\) square feet.
For the lower triangle: \(b = 12\) ft, \(h = 3\) ft. So, \(A_{lower}=\frac{1}{2}\times12\times3 = 18\) square feet.
The total area of the non - green triangles is \(A_{non - green}=36+18=54\) square feet.

Step3: Calculate the area of the green part

\(A_{green}=A_{rectangle}-A_{non - green}\)
\(A_{green}=108 - 54\)

Answer:

\(54\) square feet