In a regular triangular prism ABCA1B1C1, AA1 = 4 cm, AB = 2 √3 cm. Find the volume of the prism.
| May 16, 2021 | education
Let’s draw the height BH in the triangle ABC and determine its length.
By condition, triangle ABC is equilateral, then BH = a * √3 / 2, where a is the side of an equilateral triangle.
BH = 2 * √3 * √3 / 2 = 3 cm.
Determine the area of the triangle ABC.
Sас = АС * BН / 2 = 2 * √3 * 3/2 = 3 * √3 cm2.
Let’s define the volume of the pyramid.
V = Sаvs * АА1 = 3 * √3 * 4 = 12 * √3 cm3.
Answer: The volume of the pyramid is 12 * √3 cm3.
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