Answer:
LA = 96
SA = 108
Step-by-step explanation:
The lateral surface area is the area of the sides (not including the bases). For a triangular prism, the bases are the triangles.
The sides consist of three rectangles. The vertical rectangle is 3 by 8 units. The horizontal rectangle is 4 by 8 units.
The slanted rectangle has a length of 8 units, but we don't know the width. To find that, we use Pythagorean theorem to find the hypotenuse of the triangles.
c² = a² + b²
c² = 3² + 4²
c = 5
So the lateral surface area is:
LA = (3)(8) + (4)(8) + (5)(8)
LA = 96
The total surface area is the lateral surface area plus the area of the bases.
SA = 96 + ½(3)(4) + ½(3)(4)
SA = 108
There are 12 inches in 1 foot. You know that the area of a square is or base times hight. A square has the same base and height. So we can say (base)^2. If the base is 12 inches in this case 12^2 = 144. Answer: 144 square inches.
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