Answer:
One way to do this is to use a net, since a net is a two-dimensional representation of a three-dimensional solid, or an unfolded picture of a solid.
Explanation:
The formula A = 1/2bh is used to find the area of the two triangular faces, where A = area, b = base, and h = height. The formula A=lw is used to find the area of the three rectangular side faces, where A = area, l = length, and w = width.
Since we know that b = 4 cm and h = 6 cm, you can use that information to find the area of the triangular faces.
A = 1/2(4)(6)
A = 1/2(24)
A = 12 cm
Now since there is no other measurements for the other triangular face we assume they are the same size. Since the faces are the same size you can just double the area for the first triangular face.
The two triangular faces' area:
A = 12(2)
A = 24 cm
Now we need to find the area of all the rectangular faces.
To do this we need to use the formula A = lw
Since we know for the top two rectangular faces l = 12 cm and w = 7 cm
So for the top two rectangular faces A = 12(7)
A = 84 cm
Since there are two rectangular faces with the same width measurement you would double the area.
So instead of A = 84
A would = 84(2)
A = 168 cm
Now remember this measurement is for the top two rectangular faces.
To find the area of the bottom rectangular face we have to use
l = 12 cm and w = 4 cm
A = 12(4)
A = 48 cm
Now to find the total surface area of the prism we have to add up all the measurements we calculated.
Prism Surface Area = 24 cm + 168 cm + 48 cm
A = 240 cm²
You can also use one formula to calculate the surface area of a triangular prism which can save time over the process of using a net to derive the areas:
SA = bh+(s1+s2+s3)H
where b = base; h = height of the triangle; s1, s2, and s3 = the length of each side of the triangle base, and H = the height of the prism (which is the length of the rectangles).
SA = 4(6) + (4+7+7)(12)
SA = 24 + 18(12)
SA = 24 + 216
SA = 240 cm²
So the surface area of the triangular prism is 240 cm²