live4dramaoy0yf9
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  • 02-05-2019
  • Mathematics
contestada

A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!

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Paounn
Paounn Paounn
  • 02-05-2019

Answer:

4046.56 cm3

Step-by-step explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.

Your volume will be [tex]5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]

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