# Area of bounded region question

A square ABCD is inscribed in a circle of unit radius. semicircles are described externally on each side with the side as a diameter. the area of region bounded by four semicircle and the circle is

• For all geometry questions a picture is more helpful than a description. Additionally include what you have tried. – P. Siehr Sep 11 '17 at 9:49
• A diagram would help – neonpokharkar Sep 11 '17 at 9:50
• this guy explains it here ;- youtu.be/0_mJQ4Y_QMY?t=17m53s I did not understand the part " the area of region bounded by four semicircle and the circle" . The area of the region he calculated is not bounded by the circle. – user2625361 Sep 11 '17 at 9:53

## 1 Answer

The second sentence still misses some words, to make any sense. Using google resulted in:

Semicircles are described externally on each side with the side as a diameter.

And the following picture was also linked. You could have included such a picture in your question! In your next question also show what you have tried so far. (Also, a non-English video is not really helpful.)

I will give you the tools to solve the problem. Your task is to understand this answer, and do the calculation.

The area that should be calculated is the area between the red circle and the blue circles. Hence we need to calculate:

• $A_{blue}$, area of one blue circle.
• $A_{red}$, area of the red circle.
• $A_{square}$, area of the square.

Then the desired area is given by: $$4\cdot\frac{A_{blue}}{2} - (A_{red}-A_{square})$$ The factor 4 is due to the fact that there are 4 blue circles. The factor $\frac{1}{2}$, since we need the semi-circles.

We know that the dashed line, connecting B and the center, has length 1. Hence, we can calculate $A_{red}$.

Using Pythagorean's theorem, you get $\overline{AB}$, and you can calculate $A_{blue}$ and $A_{square}$.

• Ignore my previous question in this comment. Thanks again for the answer. – user2625361 Sep 11 '17 at 10:43
• @user2625361 Uhm, that is exactly what is written in the sentence, that you quoted, isn't it? The area of the region bounded by the four smaller semi-circles and the big circle. Have a look at the picture in my answer. It is the only region that is bounded by those circles. – P. Siehr Sep 11 '17 at 10:50
• Yeah, I finally googled the meaning of bounded. I initially though bounded meant overlapping. Sorry, my English is not good. Again thanks for answering my incomplete and gibberish question. – user2625361 Sep 11 '17 at 10:51