SOLUTION: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.

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Question 318522: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.
Found 3 solutions by Earlsdon, mananth, Fombitz:
Answer by Earlsdon(6294) About Me  (Show Source):
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You could use Heron/Hero's formula for finding the area of a triangle when you know the lengths of the three sides, a, b, and c.
A+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 s = the semi-perimeter of the triangle.
s+=+21%2F2
s+=+10.5
a+=+b=c+=+21%2F3 =7 Make the appropriate substitutions:
A+=+sqrt%2810.5%2810.5-7%29%2810.5-7%29%2810.5-7%29%29
A+=+sqrt%2810.5%283.5%29%5E3%29
A+=+sqrt%2810.5%2842.875%29%29
A+=+sqrt%28450.1875%29
A+=+21.2sq.in. (Rounded to one decimal place.)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
perimeter of equilateral triangle = 21
side = 7
s=21/2
area = sqrt{s(s-a)(s-b)(s-c)}
area=sqrt{21/2(21/2-7)^3}
area = 21.2 sq.in

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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A=%281%2F2%29bh
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Find h using the Pythagorean theorem.
h%5E2=s%5E2-%28s%2F2%29%5E2
h%5E2=s%5E2%2F2
h=%28sqrt%282%29%2F2%29%2As
A=%281%2F2%29s%28sqrt%282%29%2F2%29s
A=%28sqrt%282%29%2F4%29s%5E2
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Find s using the perimeter.
P=3s=21
s=7
Substitute,
A=%2849%2Asqrt%282%29%29%2F4 or approximately,
A=17.324
The area is 17.3 sq. inches.