Wrapping a gift box
Initial explanation
We want to find the surface area of the box, this is going to be the least amount of wrapping paper:
The total surface area is given by:
Total = area 1 + area 2 + area 3 + area 4 + area 5 + area 6
Since all the faces are rectangles, each area is given by the product of their sides:
each area = side 1 x side 2
Area 1
We have that
side 1 = 2 in
side 2 = 8 in
Then
area 1 = 2 in x 8 in = 16 in²
area 1 = 16 in²
Area 2
We have that
side 1 = 4 in
side 2 = 8 in
Then
area 2 = 4 in x 8 in = 32 in²
area 2 = 32 in²
Area 3
Is equal as Area 1:
area 3 = area 1 = 16 in²
Area 4
Is equal as Area 2:
area 4 = area 2 = 32 in²
Area 5
We have that
side 1 = 4 in
side 2 = 2 in
Then
area 5 = 4 in x 2 in = 8 in²
area 5 = 8 in²
Area 6
Is equal as Area 5:
area 6 = area 5 = 8 in²
Total area
We have that:
Total = area 1 + area 2 + area 3 + area 4 + area 5 + area 6
↓
Total = 16 in² + 32 in² + 16 in² + 32 in² + 8 in² + 8 in²
= 112 in²
Answer: 4) 112 in²
