Hi, I am really stuck on this question ,
fig.19.2 shows a template whose area is 50 square centimetres. find the total length of the template.
I have drawn the image on paint and have attached it, but its not a very good drawing. sorry if it does not make much sense to you!
I would be able to work this out if it was just the square but because there’s also this semi-circle shape attached to the square i don't really know how to calculate the length of it.
let us denote the side of the square by x.
The area of the square is .
From your drawing I understand that there's a half circle on the rightmost side of the square, so basically the diameter of the circle equals the side of the square (x). We know that the area of a circle is:
where r is the radius of the circle (the diameter is twice the radius).
So we can express the area of the half circle using x, like so:
the area of the template is the sum of the square area and the half circle area, and that's how we get the first equation, I hope that you can figure out the second equation now.