Chrissy is making a bird box for her backyard. What is the Surface area of the nesting box, including the hole? What is the surface area of the width of 7.5 inches is doubled? What is the surface area of the width 7.5 inches is half as great? L=5.5in., W=7.5in., H=9in.

Answer:Part a) [tex]SA=316.5\ in^2[/tex]Part b) [tex]SA=534\ in^2[/tex]Part c) [tex]SA=207.75\ in^2[/tex]Step-by-step explanation:Part a) Find out the surface areaThe surface area of a rectangular prism is equal to[tex]SA=2B+PH[/tex]whereB is the area of the baseP is the perimeter of the baseH is the height of the prismFind the area of the base B[tex]B=(5.5)(7.5)=41.25\ in^2[/tex]Find the perimeter of the base P[tex]P=2(5.5+7.5)=26\ in[/tex]we have[tex]H=9\ in[/tex]substitute the values in the formula[tex]SA=2(41.25)+26(9)[/tex][tex]SA=316.5\ in^2[/tex]Part b) What is the surface area if the width of 7.5 inches is doubled?we have thatThe new width is 2(7.5)=15 inFind the area of the base B[tex]B=(5.5)(15)=82.5\ in^2[/tex] ---> the area of the base is doubledFind the perimeter of the base P[tex]P=2(5.5+15)=41\ in[/tex]we have[tex]H=9\ in[/tex]substitute the values in the formula[tex]SA=2(82.5)+41(9)[/tex][tex]SA=534\ in^2[/tex]Part c) What is the surface area if the width 7.5 inches is half as great?we have thatThe new width is 0.5(7.5)=3.75 inFind the area of the base B[tex]B=(5.5)(3.75)=20.625\ in^2[/tex] Find the perimeter of the base P[tex]P=2(5.5+3.75)=18.50\ in[/tex]we have[tex]H=9\ in[/tex]substitute the values in the formula[tex]SA=2(20.625)+18.50(9)[/tex][tex]SA=207.75\ in^2[/tex]