Answer:
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
<u>Here are your fill-ins:</u>
r = 1 is a zero, so (r-1) is a factor.
r = -1 is a zero, so (r+1) is a factor.
The remainders from synthetic division are 0 each time.
See the attachment for the synthetic division numbers.
_____
The reduced quadratic is ...
... x² -6x +13 = 0
Solving by completing the square, we have ...
... (x -3)² = -4
... x = 3 ± 2i
_____
The quadratic formula would tell you ...
... x = (-(-6) ± √((-6)² -4(1)(13)))/(2·1) = (6±√-16)/2 = 3±2i
