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

Question

fredd [130]

3 years ago

15

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!!

Mathematics

1 answer:

maks197457 [2] · Answer 1 · 2022-02-10T17:20:55+03:00

maks197457 [2]3 years ago

7 0

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 $\frac{360} 5 = 72°$ . Each of the other angle is $\frac{180-72} {2} =54°$ . From there, you can calculate the height of each base triangle as in $\frac {h} 7 = tan54$ or 9.634...cm.

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