What is the surface area of this design?

Surface Area of Design = 256 in.²

Step-by-step explanation:

Given: a Shape which is made by placing two cuboid on one another.

To find: Surface area of shape.

Figure is attached.

Surface Area of Design

= Lateral Surface Area of Base Cuboid + Lateral Surface area of Top Cuboid + Area of rectangle CDLJ + Area of rectangle EFNM + Area of rectangle ABHG

Dimensions of Base Cuboid:

Length, CJ = 8 in.

Width, CD = LJ = MN = 5 in.

Height, AD = 4 in.

Dimensions of Top cuboid:

Length, HI = BI - BH = 8 - 4 = 4in.

Width, GH = KI = MN = 5 in.

Height, FH = JN - JI = 8 - 4 = 4 in.

Length of rectangle ABHG, AB = 5 in.

Width of rectangle ABHG , BH = 4 in.

Length of rectangle DCJL, DC = 5 in.

Width of rectangle DCJL , CJ = 8 in.

Length of rectangle EFNM, EF = 5 in.

Width of rectangle EFNM , FN = 4 in.

Lateral Surface Area of Base Cuboid = 2 × Height ( length + Width )

                                                              = 2 × 4 ( 8 + 5 )

                                                              = 8 ( 13 )

                                                              = 104 in²

Lateral Surface Area of Top Cuboid = 2 × Height ( length + Width )

                                                              = 2 × 4 ( 5 + 4 )

                                                              = 8 ( 9 )

                                                              = 72 in²

Area of rectangle DCJL = length × breadth

                                        = 5 × 8

                                        = 40 in.²

Area of rectangle ABHG = length × breadth

                                        = 5 × 4

                                        = 20 in.²

Area of rectangle EFNM = length × breadth

                                        = 5 × 4

                                        = 20 in.²

⇒ Surface Area of Design = 104 in.² + 72 in.² + 40 in.² + 20 in.² + 20 in.²

                              = 256 in.²

Therefore, Surface Area of Design = 256 in.²

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.