The amount of paint required by Madeline will be 0.8325 gallons
Given that
[tex]1cm=1.5ft[/tex]
We will first find the area of the wall
Area of the wall = Area of trapezoidal shape+ Area of triangular shape
Area of trapezoid = [tex]\dfrac{a+b}{2} \times h[/tex]
a= 4cm
b=14cm
h=10cm
putting this values
[tex]A=\dfrac{4+14}{2} \times 10[/tex]
[tex]A=90cm^{2}[/tex]
Area of triangular shape= [tex]\dfrac{1}{2} \times width\times height[/tex]
width=14cm
height=8cm
putting the values
[tex]A=\dfrac{1}{2} \times 14\times 8=58cm^{2}[/tex]
[tex]Total area of the wall= 90+58=148cm^{2}[/tex]
since we have
[tex]1cm=1.5ft[/tex]
[tex]148cm^{2} = 148\times (1.5)^{2} =333 ft^{2}[/tex]
Now
[tex]1gallon = 400ft^{2}[/tex]
so for [tex]333 ft^{2}[/tex] amount of paint in gallons required will be
[tex]1ft^{2} =\dfrac{1}{400} gallons[/tex]
[tex]333ft^{2} =\dfrac{333}{400} gallons=0.8325gallons[/tex]
Thus the amount of paint required by Madeline will be 0.8325 gallons
To know more about the area of trapezoid follow
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