Answer:
27√3 km²
Step-by-step explanation:
You want the area of an equilateral triangle with apothem 3 km and side length 6√3 km.
Area
Using the perimeter and apothem, one can find the area of a regular polygon using the formula ...
A = 1/2Pa . . . . . . where P is the perimeter, and 'a' is the apothem
The perimeter of an equilateral triangle is 3 times the side length.
For the given dimensions, the area is ...
A = 1/2(3·6√3 km)(3 km) = 27√3 km²
The area of the triangle is 27√3 km².
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Additional comment
The area of an equilateral triangle can also be found from the side length (s) using ...
A = (√3)/4·s²
A = (√3)/4·(6√3)² = (108√3)/4 = 27√3 . . . . . as above
