The surface area of the considered right triangular prism using its net is obtained as 96 sq. units.
What is a triangular prism?
Suppose you've got a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
For this case,
S = Surface area of prism = Area of those two symmetrical triangles and that one big rectangle.
Considering the image attached below, we get:
S = 2(Area ABJ) + Area CDHI
For triangle ABJ, the side AB is same as CB and therefore same as DE. It is because when this whose surface closes to make the prism, then AB and CB coincide, and that CB and DE are opposite sides of rectangle, so of same measure. Thus, Length of AB = |AB| = |CB| = |DE| = 3 units
|BJ| = |EG| = 4 units.
AB is height of ABJ, and BJ is base, so we get:
[tex]Area_{ABJ} = \dfrac{1}{2} \times |AB| \times |BJ| = \dfrac{1}{2} \times 3 \times 4 = 6 \: \rm unit^2[/tex]
One side of CDHI is of 7 units, and other is of (3+4+5 = 12 units).
Thus, [tex]Area_{CDHI} = 7 \times 12 = 84 \: \rm unit^2[/tex]
Thus, we get:
[tex]S_{prism} = 2(Area_{ABJ}) + Area_{CDHI}\\S_{prism} = 2(6) + 84 = 96 \: \rm unit^2[/tex]
Thus, the surface area of the considered right triangular prism using its net is obtained as 96 sq. units.
Learn more about lateral surface area of triangular prisms here:
https://brainly.com/question/15434771
