Area of this shape

Does anyone know how to work out the area of this shape??

info: it's all the info that i was given
Dimension : millimetres
From left to right : 301mm
From top to bottom: 307mm




http://img27.imageshack.us/img27/9776/shapek.jpg

 

assume angle is 45

X = ?
Y = ?
Z = 70 mm given

sin 45 x Y/Z (70)
Y = Sin 45 x 70 mm = 49.5 mm
Y= 49.5 mm

pythagoras
70(2) - 49.5(2) ---> √ ans = 49.5 mm
X = 49.5 mm

So (49.5 x 49.5) x 2 = 4900.5 mm2
301 x 307 = 92 407 mm2

92 407-4900.5 = 87506.5 mm2

Dunno if this is right -mellow

Edit: n.v.m. this is wrong

 

yup!! spot on =.= *hides in shame*

 

From left to right : 301mm
From top to bottom: 307mm
Arent it suppose to be the same lenght? cause it's a octagon right :s

 

regular octagon was ment to have same length ... but this one is irregular

 

this page should help you find the length of one of the sides

http://mathcentral.uregina.ca/QQ/database/QQ.09.05/robert3.html

from that you can work out the area of each little triangle in the corners

then all you have to do is (301 x 307) - (4 x triangle area) = area of octagon

havent actually tried it so dunno if it works, but sounds reasonable

 

its really what shadowchi did.. but slightly differ... in the end u wud still get the same answer

yes.. it would be a longer way as some lengths of the trapezium is missing .. but thank you anyways ^_^

 

^ hmmm dunno, shadowchis way assumes an angle, whereas the method (i think) on that page may not require one

well the way forward is to find the length of the sides and thats all you need to find out to move onto the area

 

basically same as shadowchi's... but this is how i'd do it:


area = (rectangle) - (4*triangles)

sides of trianges - using pythagoras:

a^2 + b^2 = c^2 ---> a=b therefore 2(x^2) = 70^2 = 4900

x^2 = 2450
x = 49.497 (3 d.p)

area of a triangle = 0.5ab*sinC

therefore: --> 0.5 * x^2 * sin90 = 0.5 * 2450 * 1 = 1225mm^2

total area = area of rectangle - 4*area of triangle

(301 * 307) - (4 * 1225) = total area
(92407 ) - (4900) = 87507mm^2

same answer

 

why's everyone making so complicated??
assuming the triagles are 45 degrees, then the area is rectangle minus square.
301 x 307 - 70 x 70 = 87507mm^2

 

but as far I can see the angles aren't 45 degrees. Returns when I have the time with a better
answer
EDIT:


My first idea was just looking at one of the edges (since the result should be just this area times 4).
The problem are the sides h and b. Most ppl here are saying the angles in the hxbx70 triangle are 45 degrees, but that also means assuming h = b with the original drawning didn't said anything about.
I started to calculate:
h^2 + b^2 = 4900 <=> b = squareroot(4900 - h^2) , h = SR(4900 - b^2)
inset them into the equations from the drawning:
y = 150,5 - b = 150,5 - SR(4900 - h^2)
x = 153,5 - h = 153,5 - SR(4900 - b^2)

since h = 153,5 - x and b = 150,5 - y:

y = 150,5 - b = 150,5 - SR(4900 - (153,5 - x)^2)
x = 153,5 - h = 153,5 - SR(4900 - (150,5 - y)^2)

Now we have two equations with two unknown, it is just insetting the bottom equation with into the upper one with y (or the other way) and isolate x or y (a calculator would be nice here). Afterwards find h and b --> find the area of the triangle ect. and finally time the result with 4.
I'm not going to do that since it be quite nasty to write it all down.

I hope I didn't made a mistake (correct me any1 if wrong) somewhere