The will spend $33.60 (option C) to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.
Step-by-step explanation:
The given is,
Construction paper cost $0.10 per square inch
Pyramid diagram with dimensions
Step:1
Formula to calculate the area of pyramid,
[tex]Area, A = lw+l\sqrt{(\frac{w}{2}) ^{2} + h^{2} } +w \sqrt {(\frac {l} {2}) ^{2} + h^{2} }[/tex]..............(1)
Where,
l - Base length
w - Base width
h - Height of pyramid
From given,
l = 12 inches
w = 12 inches
For height of pyramid,
By using Pythagorean theorem,
[tex]Hypotenuse^{2} = Base^{2} + Height ^{2}[/tex].................(2)
For right angle triangle,
Base = [tex]\frac{12}{2}[/tex] = 6 inches
Equation (2) becomes,
[tex]8^{2} = 6^{2} + Height^{2}[/tex]
[tex]Height^{2} = 8^{2} - 6^{2}[/tex]
[tex]Height^{2} = 64 -36 = 28[/tex]
[tex]Height = \sqrt{28}[/tex]
Height = 5.2915 inches
h - 5.2915 inches
Equation (1) becomes,
[tex]A = (12)(12)+(12)\sqrt{(\frac{12}{2}) ^{2} + 5.2915^{2} } +(12 )\sqrt {(\frac {12} {2}) ^{2} + 5.2915^{2} }[/tex]
[tex]= 144+(12)\sqrt{(36+27.999)} +(12)\sqrt{(36 + 27.999)}[/tex]
[tex]= 144+(12)\sqrt{63.999}+(12)\sqrt{63.999}[/tex]
[tex]= 144+(12)(7.9999)+(12)(7.9999)[/tex]
[tex]=144+95.999+95.999[/tex]
[tex]=335.998[/tex]
≅ 336 square inches
Where,
$0.10 per square inch ( from given)
Paper cost of total figure = 336 square inches
= 336 × 0.10
= $ 33.60
Result:
The will spend $33.60 to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.