### Math Notes

Subjects

#### Solid Geometry Solutions

##### Topics || Problems

One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., an edge of 2.31 in, and a base of 1.41 sq. in. Find the altitude of the prism.

Volume of a prism can be calculated in two ways

$$V = A_{base}~x ~altitude$$

$$V = A_{right ~section}~x~lateral~edge$$

Equate both equations and isolate $$altitude$$

$$base~x ~altitude = right ~section~x~lateral~edge$$

$$altitude = \frac{A_{right ~section}~x~lateral~edge}{A_{base}}$$

$$altitude = \frac{1.29 (2.31)}{1.41}$$

$$altitude = 2.11 ~ft$$