The lateral faces of the prism are 5 rectangles with dimensions 10 by 14.
So the lateral area = 5 * 10 * 14 = 700 (in squared)
Consider one of the bases of the prism.
As shown in the figure, the pentagon is made up of 5 isosceles triangles.
The vertex of each of these 5 triangles is 360°/5=72°.
Draw the altitude, which forms 2 right triangles with angle measures 36°-54°-90°.
Let he hypotenuse be s and the altitude be h in, as shown in the figure.
x*cos54°=5
x=5/(cos54°)=5/(0.588)=8.5
then,
h=x*sin54°=8.5*(0.8)=6.8 (in)
Thus, the area of one of the 5 congruent isosceles triangles is
[tex] \frac{1}{2}*10*6.8= 34[/tex] (in squared)
The area of the pentagonal base is 34*5 = 170 (in squared)
Thus the surface area = lateral area + 2 base area
= 700+2*170 = 700+340 = 1040 (in squared)
Answer:
lateral area: 700 in squared
surface area: 1040 in squared
