Question

1. the front of your garage, except for the door, needs painting. how much area do you need to paint?

Explanation:

Step1: Divide the shape into a rectangle and a triangle

The rectangle part has dimensions: height \(h_1 = 8 - 2.5=5.5\)m and width \(w = 1.5\)m. The triangle has base \(b = 6\)m and height \(h_2=2.5\)m.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{rect}=l\times w\). Here \(A_{rect}=1.5\times5.5 = 8.25\) \(m^{2}\)

Step3: Calculate the area of the triangle

The area formula for a triangle is \(A_{tri}=\frac{1}{2}\times b\times h\). Here \(A_{tri}=\frac{1}{2}\times6\times2.5= 7.5\) \(m^{2}\)

Step4: Calculate the area of the door - free part

The area of the door is \(A_{door}=1.5\times2 = 3\) \(m^{2}\)
The total area of the front - of - garage shape (including the door) is \(A_{total}=A_{rect}+A_{tri}+(1.5\times2.5)\)
\(A_{total}=8.25 + 7.5+3.75=19.5\) \(m^{2}\)
The area to be painted is \(A = A_{total}-A_{door}\)
\(A=19.5 - 3=34\) \(m^{2}\)

Answer:

\(34\) \(m^{2}\)