Im looking for help with area of shaded region . rectangle is 35m by 14m. there is semi-circle flowerbed at eachend. the shaded area is put down to lawn. (i) i worked out combines area of the 2 flowerbeds to be 154m^ (ii) the answer is 114m it asks 'what is the perimeter of the lawn. i cant work it out!! i tried to minus area of rec. by the flower beds but to no avail ! please help me!

I'm trying to reconstruct in my mind as best as I can what you mean.

i) For the area of the flowerbed, you can calculate the area of the rectangle, and then combine the two semicircles to make a circle and calculate the area that way. (or find the area of one half-circle and multiply by 2)

ii) This one is trickier. I'm assuming the semi-circles are positioned on the shorter ends of the rectangle. Hence the 'exposed' sides of the rectangle are 35 and 35 = 70. Now all we are left with is to calculate are the 'exposed' sides of each semi-circle.

but think about combining the two semi-circles again to make a full circle. do you know a formula which gives the perimeter of a circle with diameter 14?

Yes the flowerbeds are inside the rectangle at the shorter ends. yes the length ways of the rectangle is 35 then the height is 14. eh i dont think so just the regular 2 pi r for radius or maybe pi d (diameter) or what about pi r for perimeter of semi circle? sorry for incompetence

No need to be sorry; learning mathematics is a lifelong experience that takes years of purposeful practice.

You are correct. Here is the reasoning:

Since diameter is equal to double the radius, we have that the circumference of a circle is: pi * d OR pi * 2r.
Since a half circle has half the circumference of a circle, the circumference of a half circle is : (1/2)(pi)(2r) = pi*r

Adding the sides of the rectangle and the arcs, we get

[ 'exposed' sides of rectangle ] + [ 'exposed' sides of semicircles ]
= [ 35 + 35 ] + [pi*7 + pi*7]
= approximately 114