Question

THIRTY POINTS!

Answer 1

The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.        

Step-by-step explanation:

The given is,

                    Shane wants to paint,

                     4 rectangular sides

                     2 triangular sides

Step:1

           From the given diagram,

          Total surface area of paint = (4 Rectangular sides surface ares) +

                                                            (2 triangular sides surface area)....(1)

Step:2

          Surface area of 4 rectangular sides,

          For Left side(rectangle) surface area,

                                                      $A =lb$...........................................................(2)

         From the given diagram.

                                                         = (45.5 × 20)

                                                         = 910 Square feet

         Dimensions of left side and right side are equal, so area of right side equal to the left side.

                          Area of right side = 910 square feet

          Area of left and right sides,

                                                        = Left side area+ Right side area

                                                        = 910 + 910

                                                        = 1820 square feet

       For front side area,

                                                    $A =lb$...........................................................(3)

       From the given diagram,

                                                       = (24 × 20 )

                                                       = 480 square feet

      Dimensions of front side and back sides are equal, so area of front side equal to the back side.

                          Area of front side = 480 square feet

          Area of front and back sides,

                                                        = front side area+ back side area

                                                        = 480 + 480

                                                        = 960 square feet

       Surface area of rectangular sides,

                           = Area of left and right sides + Area of front and back sides

                          =  1820 + 960 = 2780 square feet

Step:3    

          Surface area of 2 triangular faces,

          For area of triangular sides,

                                              $A = \frac{hb}{2}$...............................................(4)

        From the given values,

                                                 = $\frac{(8)(24)}{2}$

                                                 = $\frac{192}{2}$

                                                 = 96 square feet

           Dimensions of front side triangle and back side triangles are equal, so area of front side triangle equal to the back side triangle.

           Area of front side triangle = 96 square meters

           Area of front and back side triangles,

                                           = front side triangle area+ back side triangle area

                                           = 96 + 96

                                           = 192 square feet

Step:4

            From the equation (1),

            Total surface area of paint = 2780 + 192

           Total surface area of paint = 2972 square feet

Result:

             The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.