How to find the area of circle if only perimeter given?
Hi,
Please help me find the answer to this, getting really confused.
The perimeter of a semi circle is 49.7cm, find the area to the nearest square millimetre?
I cant work out how to get the radius or diameter to do the Area = pi x r^2 calculation.
Thanks
Just to clarify i need to find the AREA OF THE SEMI CIRCLE.
I have the PERIMETER OF THE SEMI CIRCLE
P = π r + 2 r
49.7 = r ( π + 2 )
r = 49.7 / 5.14
r = 9.67
A = π r ² / 2
A = π (9.67 ² ) / 2
A = 147 cm ²
Circumference= 2*pi*r
area=pi*r^2
solve for radius using the circumference then plug it into the area formula
If you’re solving for a semi circle, divide the resulting area by 2
References :
well the area of the semi circle is πr^2 and you are given the perimeter which is equal to πr so πr=p where p is the perimeter you can just substitute on in and you get that
Area=π*(p/π)^2=p^2/π and you can just plug in your value for the perimeter, make sure to convert to mm first!!
References :
You know the Perimeter (or circumference) is C = πD = 2πR
You know the Area is A = πR²
From C = 2πR, R = C/2π
and
A = π(C/2π)² = C²/(4π)
References :
We know 2πr = perimeter of circle.
or, 2πr = 49.7
or, r = 49.7 x 1/2 x 7/22 [as π = 22/7]
or, r = 7.91 (approx)
Now, area of circle = π.r² = 22/7 x (7.91)² = 196.64 (approx)
So, area = 196.64 cm²
References :
Ha! They all have it wrong.
The Circumference of a semi circle is pi*r + 2*r. You then solve for r when the circumference is 497mm.
This gives you r=497mm/(pi+2). So r=96.7mm
The area of a semi circle is (1/2)*pi*r^2, since it is half a circle.
So the area in square millimetres is 14677 square millimetres.
References :
P = π r + 2 r
49.7 = r ( π + 2 )
r = 49.7 / 5.14
r = 9.67
A = π r ² / 2
A = π (9.67 ² ) / 2
A = 147 cm ²
References :