2. ## Re: Equation help

Dear all, this question has stumped me. If anyone has the formula, I would be very grateful.

3. ## Re: Equation help

Hello, fleurdel!

The figure below is made up of a square of side 28 cm.
One semicircle and one quadrant are drawn inside the square.
Given that the total area of portions A and C is two times the area of B,
find the area of B. .$\displaystyle \left(\text{Take }\pi = \tfrac{22}{7}\right)$

Code:
        *-*-*-------------*-*
|        *  A *     |
|           *    B  |
|          *   *    | 14
|                   |
|         *      *  |
|         *       * +
|         *   C     |
|                  *|
|     D    *        | 14
|           *       *
|             *     *
*-----------------*-*
28

$\displaystyle \text{(Area of }A+B) \;=\;\text{(Area of the square)} - \text{(Area of the quadrant)}$

. . . . . . . $\displaystyle A + B \;=\;28^2 - \tfrac{1}{4}\pi(28^2) \;=\;784 - 196\pi$ .[1]

$\displaystyle \text{(Area of }B+C) \;=\;\text{(Area of semicircle)}$

. . . . . . .$\displaystyle B + C \;=\;\tfrac{1}{2}\pi(14^2) \;=\;98\pi$ .[2]

. . $\displaystyle \underbrace{A + C}_{\text{This is }2B} + 2B \;=\;(784-196\pi) + 98\pi$

. . . . . . $\displaystyle 4B \;=\;784 - 98\pi$

$\displaystyle \text{Therefore: }\:B \:=\:196 - \tfrac{49}{2}\pi \:=\:196 - \tfrac{49}{2}\left(\tfrac{22}{7}\right)$
. . . . . . . . $\displaystyle B \;=\;119\text{ cm}^2$

4. ## Re: Equation help

Thank You, Soroban, that was awesome!!!