THIRTY POINTS!
Shane plans to paint his barn. He will paint the 4 rectangular sides: left, right, front including the door, and back. He will also paint the 2 triangular sections formed by the roof with a height of 8 ft. He will not paint the 2 rectangular sections of the roof. Calculate the total number of square feet of surface area that Shane will paint

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,

                                                      ...........................................................(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,

                                                    ...........................................................(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,

                                              ...............................................(4)

        From the given values,

                                                 =

                                                 =

                                                 = 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.              

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.