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# What is the area in square units of the triangles described?

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Find the area (in square units) of each triangle described.

1.  a = 1, b = 1, c = 1

2.  a = 49, b = 33, c = 18

Apr 17, 2019

#1
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Hi, thanks for posting. We will use heron's formula for this, because I assume if you posted on this forum you would have already had googled a triangle area calculator.

Heron's Formula is:

$$A=\sqrt {s(s-a)(s-b)(s-c)}$$

$$s$$: The Semiperimeter of a triangle (Half of the perimeter)

$$a,b,c$$ = The sides of the triangle.

First Question:

$$A=\sqrt {1.5(1.5-1)(1.5-1)(1.5-1)}\\A=\sqrt {1.5(.5^3)}\\A=\sqrt {0.1875}\\A \approx \boxed{0.433}$$

Second Question:

$$A=\sqrt {50(50-49)(50-33)(50-18)}\\A=\sqrt {50(544)}\\A=\sqrt {27200}\\A \approx \boxed{164.92}$$

Specify if you want a certain formula used, thanks.

Apr 17, 2019
edited by Bxtterman  Apr 17, 2019
edited by Bxtterman  Apr 17, 2019
#2
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I'm sorry, but I'm not quite getting something.

In the 1st question you used s = half the perimeter

In the 2nd question you used s = the entire perimeter  (i.e., 49+33+18=100)

Could you clarify that for me, please?

?

Guest Apr 17, 2019
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The second one has a little error.

It should use 50 not 100.

Melody  Apr 17, 2019
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My Bad! I was too carred away by the LaTeX

Bxtterman  Apr 17, 2019
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My fault! Sorry! :(

Bxtterman  Apr 17, 2019
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Hi Bxtterman,

It is absolutely not a problem.

It is actually good that little errors like this are made from time to time.

Askers should be checking our answers and they should have enough knowledge to locate errors such as this for themselves.

I often do not check my answers and this is a part of the reason.

It is really good that our guest found this error and reported his/her confusion.

Welcome to our web2.0calc forum by the way.

I have already noticed you making some great contributions.

Melody  Apr 18, 2019
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Thanks! I'll try to answer 1-2 questions per day.

Bxtterman  Apr 18, 2019
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1. As you can use Heron's formula for the first question, we have an equilateral triangle since a=b=c=1.

The formula to find the area of an equilateral triangle is $$\frac{\sqrt{3}}{4}s^2$$, so we have  $$\frac{\sqrt{3}}{4}1^2=\frac{\sqrt{3}}{4}\approx\boxed{0.433}.$$

2. Using Heron's Formula, we have: $$\sqrt{(50)(50-49)(50-33)(50-18)}=40\sqrt{17}\approx\boxed{164.92}.$$

Apr 17, 2019