Area and Circumference issue

[siyanor]

lets say we have above image(numbers are in meter), which is containing an octagonal (A) and 4 semicircular(B),now we are suppose to:
1)calculate the Area and circumference of field(A+B) in x expression ?
2)for what value of x , areas and circumferences of A and B are equal(not counting diameter in B)?
3)for x equal to 5 how many tree with the distance of 2 meters between each , we can have ?

Answer :
1)for the first one we will calculate the area and circumference of A and B then sum of them will be the Area and Circumference of required field

2)i know that we have to equal the Area and Perimeter to find the value of x but,does the question is asking us to find the x for Area and Perimeter of the whole field or we have to do it once for A and once for B (and would someone please explain who the heck we can find the Area or circumference of a semicircle without it diameter?!!!)
3)in this question we have to calculate the Perimeter of the field (around the A and B )we have the perimeter of the the rectangle part as (2((60-2x)+(40-2x)) and length of 4 arcs we have :

we will substitute 5 in the formula to find the numbers of trees.

Is the above calculation make sense?can you help me out on the question number 2?

 

[tkhunny]

I think you're about 28% low on the Area. How did you manage your result?

 

[siyanor]

Hey there,

Thank you for replying.
First of all i cant see my post, is this normal ?

Regarding the results :
Area of Polygon=Area of Rectangle - 4*area of triangle= 2400-2x2
Area of semicircle : we have diameter as x(sqrt2)so our radius will be half of that.we have in total two circle so 2*(pi*r^2)= 2(pi*(xsqrt2/2)^2)

Perimeter of polygon= perimeter of rectangle - 4 *perimeter of a triangle + 8*hypotenuse
Perimeter of polygon = 2*(40+60)-4(2x+(xsqrt2))+8*(xsqrt2)=200+(4sqrt2-8)x

Perimeter of semicircles = 4*((2(Pi)(r)/2+2r)=4(Pi(sqrt2)x/2+x(sqrt2))=2(sqrt2)(Pi + 2)x

is there anything wrong with my calculation ?Please correct me if i am wrong.

Thank you

 

[tkhunny]

I guess I don't comprehend the drawing. I was thinking:

1) Giant Rectangle
2) LESS four triangular corners
3) PLUS four semi-circular regions.

 

[tkhunny]

I guess score one for Internet Explorer 9.0?