Answer:
Explanation:
Part A
A square pyramid surface area can be calculated using A = Lw (which gives you surface area of the base square) & 4 of A = bh/2 (which gives you surface area of the 4 triangles on the side)
This means overall A = Lw + 4(bh/2)
Length = L = 4"
Width = w = 4"
Base = b = w = L = 4"
Height = h = 6"
A = Lw + 4(bh/2)
A = Lw + 2bh This is the answer after simplifying
A = (4")(4") + 2(4")(6") This is the numerical expression.
A = 16" + 48" = 64" This is the numerical answer.
A square prism surface area can be found using 2 of A = Lw (which represents the surface area of the 2 squares) and 4 of A = Lh (which gives you the surface area of the 4 rectangles).
This means overall A = 2Lw + 4Lh
Length = L = 4"
Width = w = 4"
Height = h = 6"
A = 2Lw + 4Lh
A = 2(4")(4") + 4(4")(6") This is the numerical expression.
A = 128" This is the numerical answer.
Part B
To see the difference between the 2 polyhedrons, I will place them as follows.
Pyramid Area = A = (4")(4") + 2(4")(6")
Prism Area = A = 2(4")(4") + 4(4")(6")
The numerical expression shows that the surface area of the prism has one more square area (as represented by 4"x4"), and has 2 more rectangular area (as represented by 4"x6").
The difference of the 2 numerical expressions can be found using subtraction:
A = [2(4")(4") + 4(4")(6")] - [(4")(4") + 2(4")(6")]
A = (4")(4") + 2(4")(6")
Hope this helps.