Question

the volume of this triangular prism is 126 cubic centimeters. what is the value of y? 4 cm 7 cm y y = centimeters submit

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(7\) cm and the height is \(4\) cm.

$$A = \frac{1}{2}\times7\times4=\frac{1}{2}\times28 = 14\space cm^{2}$$

Step2: Use the volume formula of a triangular prism

The volume formula of a triangular prism is \(V=A\times l\) (where \(A\) is the area of the triangular base and \(l\) is the length of the prism, which is \(y\) in this case). We know \(V = 126\space cm^{3}\) and \(A=14\space cm^{2}\).

$$126=14\times y$$

$$y=\frac{126}{14}$$

$$y = 9$$

Answer:

\(9\)