Question

Lisa glued two pieces of wood together to make the letter L in her art class. She plans to paint all sides of it purple, including the base. The longer piece of wood has dimensions of 1 inch by 1 inch by 9 inches. The shorter piece of wood has dimensions of 3 inches by 1 inch by 1 inch. How many square inches of purple paint will Lisa use to paint her letter L?
A. 50 square inches
B. 51 square inches
C. 38 square inches
D. 52 square inches

Answer 1

The 52 square inches of purple paint will Lisa use to paint her letter L, If she plans to paint all sides of it purple, including the base, the longer piece of wood has dimensions of 1 inch by 1 inch by 9 inches and the shorter piece of wood has dimensions of 3 inches by 1 inch by 1 inch.

Step-by-step explanation:

The given is,

             Lisa glued two pieces of wood together to make the letter L    

             The longer piece of wood has dimensions of 1 inch by 1 inch by 9 inches.

              The shorter piece of wood has dimensions of 1 inch by 1 inch by 3 inches.

Step:1

           Surface area of L becomes,$Total surface area of L = Surface area of Longer piece + Surface area of smaller piece$            Formula for surface area of right rectangular prism,

                              $Surface area, A = 2(lw+hl+hw)$

Step:2

           For longer piece,

                                                  $A_{L} = 2(wl+hl+hw)$

        From given,

                             w - 1 inch

                               l - 1 inch

                              h - 9 inches

         Surface area of Longer piece becomes,

                                                    $= 2[(1)(1)+(9)(1)+(1)(9)]$

                                                    $= 2(1+9+9)$

                                                    $=2(19)$

                                                    $=38$

                                             $A_{L} = 38$ Square inches

Step:3

           For shorter piece,

                                            $A_{S} = 2(wl+hl+hw)$

        From given,

                             w - 1 inch

                               l - 1 inch

                              h - 3 inches

         Surface area of Longer piece becomes,

                                                    $= 2[(1)(1)+(3)(1)+(1)(3)]$

                                                    $= 2(1+3+3)$

                                                    $=2(7)$

                                                    $=14$

                                              $A_{S} = 14$ Square inches

Step:4

        Surface area of L becomes,

                                                    = $A_{L} +A_{S}$

                                                    $=38+14$

                                                    = 52 Square inches

Result:

         The 52 square inches of purple paint will Lisa use to paint her letter L, If she plans to paint all sides of it purple, including the base, the longer piece of wood has dimensions of 1 inch by 1 inch by 9 inches and the shorter piece of wood has dimensions of 3 inches by 1 inch by 1 inch.