Find the volume of a regular triangular prism if the side is 7 cm and the area of the side face is 63 cm2.

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.