Question

a right triangular prism has equilateral triangles for bases. each side of the base is 4 centimeters in length and the prism has a height of 5 centimeters. what is the volume of the prism? 5 of 8 questions 5√3 cm³ √3 cm³ 4√3 cm³ 20√3 cm³

Explanation:

Step1: Calculate the area of the base (equilateral triangle)

The formula for the area of an equilateral triangle with side length \(a\) is \(A=\frac{\sqrt{3}}{4}a^{2}\). Given \(a = 4\) cm, then \(A=\frac{\sqrt{3}}{4}\times4^{2}=\frac{\sqrt{3}}{4}\times16 = 4\sqrt{3}\) \(cm^{2}\).

Step2: Calculate the volume of the prism

The formula for the volume of a prism is \(V=Ah\), where \(A\) is the area of the base and \(h\) is the height of the prism. Given \(A = 4\sqrt{3}\) \(cm^{2}\) and \(h=5\) cm, then \(V=4\sqrt{3}\times5=20\sqrt{3}\) \(cm^{3}\).

Answer:

\(20\sqrt{3}\text{ cm}^3\) (the fourth option)