# Math Help - word problem dont know were to start

1. ## word problem dont know were to start

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.

2. $
\begin{gathered}
Area_{template} = x^2 + \frac{{\pi \left( {\frac{x}
{2}} \right)^2 }}
{2} = 50 \\
Length_{template} = 3x + \frac{{\pi x}}
{2} \hfill \\
\end{gathered}
$

good luck...

3. Originally Posted by Peritus
$
\begin{gathered}
Area_{template} = x^2 + \pi \left( {\frac{x}
{2}} \right)^2 = 50 \hfill \\
Length_{template} = 3x + \frac{{\pi x}}
{2} \hfill \\
\end{gathered}
$

good luck...
I don't really understand how you got to your final 2 equations could you please explain it step my step? please

thanks!

p.s. what do I do with the length of the square? which is 6cm? where am I suppose to use that?

4. let us denote the side of the square by x.
The area of the square is $x^2$.
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:
$
\pi r^2$

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:

$
\frac{{\pi \left( {\frac{x}
{2}} \right)^2 }}
{2}$

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.

5. I kind of understand the first equation, but i am still not sure how to calculate the total length of the template, would I just add all the sides up together?

and isn't the area of the square 36cm^2 ?

6. can someone please show me how to calculate the total length , please. maths is not my best subject