Question

What is the area of an equilateral triangle with side lengths of 8 cm?

Answer 1

We need to use Pythagoras here. to find the height.

The height will be right down the middle.

Half of 8 = 4.

If (a^2)+(b^2)=c^2

You know a^2 is 4 and c^2 is 8.

b^2= c^2-a^2

b=8−4−−−−√


8−4−−−−√=4√=2


2 is the height.

Using the formula a=bh/2

b= 8

h= 2

8*2=16

16/2=8

therefore 8 is the area of this equilateral triangle.

Answer 2

thank you

Answer 3

No.

Answer 4

@KaylaRose98
the formula for the area of an equilateral triangle with side equal to a is
\[\huge \frac{a^2\sqrt3}{4}\]

Answer 5

27.713 then?

Answer 6

Whatever that might be. I'd leave it with the \(\sqrt 3\) but if the teacher wants a decimal answer, then go for it

Answer 7

thank yo

Answer 8

you

Answer 9

can you answer my question please?

Answer 10

Might as well derive it, while you guys are watching...

Answer 11

Using the Pythagorean theorem, the height is given by
\[\huge \sqrt{a^2 - \frac{a^2}{4}} =\sqrt{a^2\left(1-\frac14\right)}=a\sqrt{\frac34}=\frac{a\sqrt3}{2}\]

Answer 12

Now, since
\[h = \frac{a\sqrt3}{2}\]and the base\[b = a\]
Then the area
\[\huge \frac{bh}2=\frac{a\times \frac{a\sqrt3}{2}}{2}=\frac{a^2\sqrt3}{4}\]

Answer 13

~27.72sq cm