Geometry help please?

Protip: regular N-gons can be divided into identical triangles, trapezoids and parallelograms can all be split in triangles and rectangles. Calculate their areas independently and add them at the end.

Also, if the angles are different, then it is not a square.

also, what is ‘K’?

@ragingloli That’s exactly my question…if it’s 4…wait…... It notes 4” on the bottom and top lines, but nothing on the side lines. So…it’s not an exact square. I also learned that about splitting them into triangles and rectangles, but not sure how to apply it.
SO….if LE is 46 degrees and VO is 45 degrees, then LE is > VO. Is that right?

Don’t know what you’re talking about with K.

here is what my book says about the pentagram case:

I will just assume that the side means the side of the base of the triangles.

so you have a = 3
φ = 360/n
A = n x An (n is the number of the triangles in the ngon)
An = ½ x r² x φ

You do not have r, so you have to calculate it:
a = 2r x sin φ/2
you already have a, so…
a / sin φ/2 = 2r
r= (a / sin φ/2) x ½

Therefore:
An = ½ x ((a / sin φ/2) x ½)² x φ
A = (½ x ((a / sin φ/2) x ½)² x φ) x n

no guarantees, though, last geometry class was years ago.

now for the hexagram

I will assume that perimeter means the sum of all sides of the hexagram and not the circumference of the circle that surrounds the hexagram

so
p = 48
and
p = n x a
therefore
p/n = a
thus
a = 8

now you have a, repeat the same procedure you did for the pentagram (remember to recalculate φ)

the triangle
A = ½ x g x h (g is the base, h is the altitude I presume)

parallelogram (I found equations without having to split it into triangles and rectangles)

A = a x b x sin α

Trapezoid

A = ½ x ( a + c ) x h

So and here is the parallelogram with triangular dissection:
A = 2×½ a x h + h x b (a is the small side of the triangle, b is 12 – a , h is the height of the parallelogram)
A = ah + hb
A = h(a+b)
A = 6sinα x ( 6cosα + 12 – 6cosα )

For the dissected trapezoid
A = ch + ((a-c)h)½ (with a the longer side, c the short side and h the height)

but as you can see
A = ch + (ah-ch)½
A = ch + ½ah -½ch
A = ½ch + ½ah
A = ½(ch+ah)
A = ½(c+a)h
it is the same as the equation I already gave you above.

@ragingloli I gotta “book” too. That’s part of the problem. I need a human to talk to.

Addition to the dissected parallelogram
A = 6sinα x (6cosα +12 -6cosα )
A = 6sinα x 12
A = sinα x 6×12

Also the same as the one in the book.
Sometimes I make it harder for myself as needed lol.

”I gotta “book” too. That’s part of the problem. I need a human to talk to.”
Any problems understanding what I wrote?

also, are the angle labels on the opposite sides of the LV diagonal?

That’s just it…they LOOK diagonal. If this isn’t a perfect square, it would take the Hubble telescope to see it….I’ll draw a picture and post it.

No problem understanding what you wrote if I have an hour to puzzle each post out. As it is, I have, maybe, 5 minutes to figure it out before I have to go help another kid with English, or Lit, or Natural Science. I need a micro-wave version.

I made some pictures for you.
Here
Here
and Here

I am way too nice to you.