A right triangular prism has 3 rectangular faces.
If each of the edges of the triangular base measures 4.5cm,
and the length (the height) of the prism is 22.5cm,
the 3 rectangular faces (sides of the box) are rectangles,
22.5cm long and 4.5cm wide.
Each face has a surface area of (22.5cm)(4.5cm)=101.25 square centimeters.
The total lateral surface area for the 3 rectangular sides of the box is
3(101.2 square centimeters)=303.75 square centimeters.
If the triangular faces of the box are triangles
with a base measuring 4.5cm and a height measuring 4.0cm,
the surface area of each triangular face is
(1/2)(4.5cm)(4.0cm)=9 square centimeters.
The surface area of the two triangular faces adds up to
2(9 square centimeters)=18 square centimeters.
The total surface area for the box is
303.75 square centimeters + 18 18 square centimeters= 321.75 18 square centimeters,
and that rounds up to highlight 322 square centimeters.
NOTE:
The answer above is the one your teacher wants,
but there is a problem with this problem.
An equilateral triangle with sides measuring 4.5cm
would have a height of approximately 3.9cm.
The Pythagorean theorem says so.
However, the 4.0cm value makes the calculations easier.
