Answers:
- Lateral Area = 96 square km
- Surface Area = 144 square km
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Step-by-step explanation:
For any prism, the base faces are parallel to one another, and they are congruent. In this case, the two triangles are the base faces.
The lateral sides are the three rectangles that form the "walls" so to speak. We can think of the base faces as the floor and ceiling.
The right-most wall is a 4 by 6 rectangle that has area 4*6 = 24 square km
The front-most wall is 8 by 4 leading to 8*4 = 32 square km area.
The back wall is a rectangle that is 10 by 4 to get an area of 10*4 = 40 square km.
The total lateral area is 24+32+40 = 96 square km
A shortcut is to compute the perimeter of the base to get 8+6+10 = 24 km, which multiplies with the height 4 to get 24*4 = 96 square km.
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Now let's compute the area of one triangle
Each triangle has a base of 8 and a height of 6. So the area is
area = 0.5*base*height = 0.5*8*6 = 24 square km
There are two of these identical triangles, so we have a total base area of 24*2 = 48 square km
Add this onto the lateral area and we get the total surface area to be 48+96 = 144 square km