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An equilateral triangle has side lengths of 40mm, what is the area of the triangle?

User Sangoku
by
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1 Answer

3 votes
equailateral means that base=40mm
solve for height
split the triangle in half with a line perpendicular to the base
now you have 2 right triangles with base 40/2=20 and hypotonuse 40
solve for height or the other side
use pythagorean theorem
a^2+b^2=c^2
20^2+b^2=40^2
400+b^2=1600
subtract 400 fromb oth sides
b^2=1200
square root boht sides
b=√1200=20√3

the height =20√3
area of triangle=1/2base times height
base=40
height=20√3

1/2 times 40 times 20√3=20 times 20√3=400√3

the area is 400√3 mm^2
User Grygoriy Gonchar
by
8.4k points

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