**[Article déjà publié le 23 août 2023]**

## What are the benefits of regularly doing math challenges?

Math challenges play a crucial role in developing cognitive and analytical skills. Regular practice of these challenges helps strengthen mathematical logic, improve abstract reasoning ability, and develop effective strategies for solving complex problems. Additionally, math challenges provide a valuable opportunity to explore advanced math concepts in a fun way, which can spark a lasting interest in math in people of all ages.

## Challenge: what is the area of the blue rectangle?

First of all, to successfully find the solution, you must add some indications to the semicircle and the rectangle, as in the figure below.

**Have you found the answer to this challenge?** Here is the reasoning!

Using the **Pythagorean theorem** in the triangle MAB, we obtain:

(r+x)^{2} + y^{2} = 6^{2}

(r+x)^{2} + y^{2} = 36

r^{2} + 2rx + x^{2} + y^{2} = 36

Considering that **the circle equation** at point M is: x^{2} + y^{2} = r^{2}We have :

r^{2 }+ 2 rx + r^{2} = 36

2 r^{2} + 2 rx = 36

r^{2} + rx = 18

r(r+x) = 18

Either **BC.AB = 18**

### Did you manage to find the correct answer?

By participating in mathematical challenges, individuals are encouraged to think creatively and innovatively to find solutions.

>> Read also: Can you solve this operation? 9 -18 ÷ 2 × 5 + (7 + 2² × 5)

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