Find the volume of a regular triangular prism if the side is 7 cm and the area of the side face is 63 cm2.
June 29, 2021 | education
| Find the volume of a regular triangular prism if the side is 7 cm and the area of the side face is 63 cm ^ 2.
The side of a regular triangular prism is the height.
In order to find the volume, you need to multiply the base area by the height.
1) The base is a triangle, the side of which is 7 cm.
2) Find the height if the side face is 63 cm ^ 2, and the width is 7 cm. The height in a regular triangular prism is the side of a rectangle, that is, the side face.
h = 63 cm ^ 2/7 cm = 63/7 cm = 9 cm.
3) Find the area of the base, that is, an equilateral triangle.
S main = a ^ 2 * √3 / 4 = 7 ^ 2 * √3 / 4 = 49/4√3 = 12.25√3 cm ^ 2.
4) Find the volume.
V = 12.25√3 cm ^ 2 * 9 cm = 12.25 * 9√3 cm ^ 3 = 110.25 * 1.7 cm ^ 3 = 187.425 cm ^ 3.
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