Question

1. find the height of the triangle sides for the triangular prism given that the surface area is 462 in². hint: there are 2 equally - sized triangles, 2 equally - sized rectangles, and 1 other rectangle.

Explanation:

Step1: Calculate areas of known - shaped faces

The area of the two equal - sized rectangles with dimensions 7.5 in and 20 in is $2\times(7.5\times20)=300$ in². The area of the rectangle with dimensions 6 in and 20 in is $6\times20 = 120$ in². Let the area of each triangle be $A_{triangle}=\frac{1}{2}\times6\times h = 3h$ in², and the area of the two triangles is $2\times3h=6h$ in².

Step2: Set up the surface - area equation

The surface area of the triangular prism $S$ is the sum of the areas of all its faces. So, $S=6h + 300+120$. Given that $S = 462$ in², we have the equation $6h+300 + 120=462$.

Step3: Solve the equation for $h$

First, simplify the left - hand side of the equation: $6h+420 = 462$. Then subtract 420 from both sides: $6h=462 - 420=42$. Divide both sides by 6: $h=\frac{42}{6}=7$ in.

Answer:

7 in