Find the Area of an Equilateral Triangle

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@mathvibe
Follow along to find the area of an equilateral triangle.

#shorts #maths #geometry #mathproblem

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Like others, I just did the Pythagorean theorem 25-6.25 = 18.75, sqrt = 4.33 x 2.5 ~ 10.825 I know junior high math

datapro

In general, for an equilateral triangle with side=s:

Area=s^2 ×√3/4

hank

Why do people think that an equation is an answer? We were not told the area of the triangle. She just stopped and did not finish the job.

PYTHAGORAS

I've no idea why you left things in terms in sin(60). That's a value we should know by the time we're answering this sort of question. Solving in general for sides of length x, that bisector has length √(x² - (x/2)²) = √3/2·x. So have √3/2·x²as the general solution. √3 · 25/2 ≅ 21.65 in your particular case.

christopheroliver

For equilateral triangles, the shortcut is (side squared ×√3/4)

musicfan

Surely you would use Pythagoras then time it by 2?

bobsmith

Second formula that also works is sqrt s(s-a)(s-b)(s-c) where s = (a+b+c)/2. S represents the sides of the triangle ❤️ Math teacher

deidrafryer

Or alternatively h bisects the bottom length. Therefore in the resulting right triangle you can use the Pythagorean theorem to calculate h. 5^2 - (5/2)^2 gives you h^2. Then h=4.33. Area = 4.33*5/2 = 10.825. No trigonometry necessary.

realnazarene

and sin60 is sqrt(3)/2 so we can use that to get to 25sqrt(3)/4.

fredsmith

Good, I need to practice more of these math problems

deborahlester

Wouldn't it be simpler to use the Pythagorean Theorem - the theorem of Euclidean geometry about right triangles. It says that in each of them, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. According to the symbols in the figure below, the following equality occurs: a2+b2=c2

waldekkaszubski

Area of Equilateral Triangle with side 5 numerical value
A = 2 [1/2 (5/2 ) a ] = 5/2 a
Sine 60* = 0.866 =a/5 therefore a = 5(0.866)
A= 5/2 X 5(0.866) =12.5 (0.866) = 10.825 square unit

marbymendez

All triangles have the same area formula which is A=(1/2)absinC. The angles can be changed.

canadaballchannel

You could always use heron's formula which works for any sort of triangle

nishilsheth

0, 866

There's actually a relation between the length of the apothem and the length of the sides of an equilateral triangle. The answer is about 0, 866. Multiply this by the length of the side and you have the length of the apothem.

It's probably been figured out before, but I actually saw this instantly when I saw your problem and I've never been taught that it was a thing. It's nice to see i'm getting smarter as I grow up and educate myself.

falashlaba