The total amount of paint required to paint the wall by Matthew, who uses scale model 1cm equal to 2.5 ft is 2.66 gallons.
What is scale factor?
Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures. It can be given as,
[tex]r=\dfrac{l_n}{l}[/tex]
Here, (l) is the length of the original figure and ([tex]l_n[/tex]) is the length of the new figure.
Matthew uses this scale model of a design he plans to paint on a wall. He uses the key,
[tex]\rm 1 \;cm = 2.5 \;ft[/tex]
Lets find out first the area of this composite figure.
All the dimension of the trapezoid will be multiplied with the 2.5 for the scale factor. Thus the area can be given as,
[tex]A=\dfrac{(14+4)2.5}{2}\times(10\times2.5)\\A=562.5\rm ft^2[/tex]
All the dimension of the triangle will be multiplied with the 2.5 for th scale factor.
The height of the triangle is,
[tex]h=18-10\\h=8\rm cm[/tex]
Thus, the area of the triangle is,
[tex]A=\dfrac{(14\times2.5)\times(8\times2.5)}{2}\\A=500\rm ft^2[/tex]
Total area of the wall is,
[tex]A=562.5+500\\A=1062.5\rm \; ft^2[/tex]
Now, one gallon of paint will cover 400 square feet (37.16 square meters) of wall. Thus the total paint required is,
[tex]\rm paint=\dfrac{1062.5}{400}\\paint=2.66\rm \;gallons[/tex]
Hence, the total amount of paint required to paint the wall by Matthew, who uses scale model 1cm equal to 2.5 ft is 2.66 gallons.
Learn more about the scale factor here;
https://brainly.com/question/10253650
