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fomenos
2 years ago
8

Find the area of an equilateral triangle (regular 3 Gon) with the given measurement 9 in perimeter a=SQ.in

Mathematics
1 answer:
blsea [12.9K]2 years ago
4 0

Answer:

3.897 in^{2}

Step-by-step explanation:

equilateral triangles are also equiangular, meaning the have equal angles.

Triangle sum theory says that angles of a triangle add up to 180.

That means each angle is 60.

A = bh/2

You need the (h). The base of is 3.  Perimeter = 9, so each side is 3

Draw a perpendicular line for the height. The line cuts the base in half (1.5)

Using trigonometry you can find the height.

tan 60° = h/1.5

h = height, 1.5 is half of 3, 60° is the base angle.

multiply each side by 1.5

1.5(tan 60°) = h

h=2.598

then substitute h into formula

A= <u>(2.598)(3) </u>

           2

A = 3.897 rounded

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