Hello, Mukilab!

Your answer to #7 is correct! . . . (well, sort of).

7) A 12-cm square has a semicircle cut out of it.

Calculate the perimeter of the shape correct to 3 decimal places. Code:

12
*-------------------*
|:::::::::::::::::::|
|:::::::::::::::::::|
|:::::::::::::::::::|
12 |:::::::* * *:::::::| 12
|:::* *:::|
|:* *:|
|* *|
| |
*---------*---------*
6 6

We want the perimeter of the shaded region.

A circle has circumference $\displaystyle 2\pi r$

The semicircle has perimeter: .$\displaystyle \tfrac{1}{2}(2\pi)(6) \:=\:6\pi$ cm.

The three sides of the square has perimeter $\displaystyle 36$ cm.

The perimeter of the shaded region is: .$\displaystyle 6\pi + 36 \;=\;54.84966692$ cm.

Correct to 3 decimal places: .$\displaystyle 54.850\text{ cm}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The problem was not clearly stated.

It did not specify that the semicircle was on the *edge* of the square

. . nor that it was the *largest* such semicircle.

In fact, there is a classic problem:

. . "Find the *largest* semicircle that can be inscribed in a square".

The solution looks like this: Code:

o ------*-*-*------o
| *::::::::::*. |
| *:::::::::::::::*
| *::::::::::::::* |
|::::::::::::::* |
*::::::::::::* |
*::::::::::o |
*::::::::* |
|::::::* |
| *::* |
o--*---------------o

I'll let *you* work on it . . .