Answer:
422[tex]cm^2[/tex]
Step-by-step explanation:
1. Approach
This problem asks one to find the surface area of the given figure. This can be done by splitting the given figure into two similar figures. Then calculate the surface area of each of the similar figures. After doing so, subtract the covered surface areas, the contact point between the two simple figures is not a part of the surface area since it is covered by the other part of the figure. Remember to take away twice the area of this contact point, since it is present on both figures.
2.Find the surface area of the first figure
The surface area of a figure is the two-dimensional space around the figure. In essence, if one were to wrap the figure in paper, the surface area is the amount of paper one would need. Find the 2-dimensional area of each side, this can be done by multiplying all combinations of two dimensions together, adding the results, and then multiplying that value by (2).
(5) * (10) = (50)
(5) * (7) = (35)
(7) * (10) = (70)
Now add thee value together,
(50) + (35) + (70)
= (155)
Double the result,
(155) * (2) = (310)
3. Find the surface area of the other figure
Now repeat the process that was used to find the surface area of the other figure for this figure.
(8) * (4) = (32)
(4) * (3) = (12)
(8) * (3) = (24)
Add the results,
(32) + (12) + (24) = (68)
Double the value,
(68) * (2) = (136)
3. Now subtract the repeated side
Now that one has the value of both simple figures, add up the value and then subtract twice the value of the repeated side.
(310) + (136) = (446)
(446) - ((2)*(4)*(3))
= (446) - (24)
= (422)
