LeAnn is purchasing giftwrap for a box that measures 8 inches long, 6 inches wide, and 6 inches tall. Calculate the total area of the box that will be covered in gift wrap. Show all of your work for full credit.
A box shape in three dimensional space. Formally, a polyhedron for which all faces are rectangles.
Rectangular Parallelepiped
Volume = lwh 866=288Lateral Surface Area = 2lh + 2wh=94Surface Area = 2lw + 2lh + 2wh=288
Let
L---------> the length side of the box
W--------> the width side of the box
H-------> the height of the box
we know that
\(L=8\ in\\W=6\ in\\H=6\ in\)
the surface area of the box is equal to
\(S=2*area\ of\ the\ base+perimeter\ of\ the\ base*H\)
Find the area of the base
\(A=L*W=8*6=48\ in^{2}\)
Find the perimeter of the base
\(P=2*L+2*W=2*8+2*6=28\ in\)
Find the surface area
\(S=2*48+28*6\)
\(S=264\ in^{2}\)
therefore
the answer is
the total area of the box that will be covered in gift wrap is \(264\ in^{2}\)