Find area of the shaded part in the given diagram

[chwala]

Homework Statement

See attached.

Relevant Equations

O level Math

In my working, i have the following approach;

Using area of semi -circle and area of sector concept;

$x +z = \dfrac{9π}{2}$
$x +y = \dfrac{9π}{2}$
$z+p = \dfrac{9π}{2}$

On solving the simultaneous equations,
$⇒x=p$

then,

$x=\dfrac {9π}{4} - \left(\dfrac{1}{2} ×3 ×3\right) = \dfrac{9π-18}{4}$

$⇒ p = \dfrac{9π-18}{4}$

Therefore,

$m+x+p = \dfrac{36-9π}{2} + \dfrac{9π-18}{4} + \dfrac{9π-18}{4}$

$=\dfrac{36-9π}{2} +2\left( \dfrac{9π-18}{4} \right)$

$=\left(\dfrac{36}{2} - 4 .5π+ 4 .5π - 9 \right)= 18-9=9$

Unless there is a better approach. Good day and cheers.

 

[Lnewqban]

Using symmetry of the individual shaded areas respect to the diagonal lines may be a simpler solution.

 

[Hill]

Homework Statement: See attached.
Relevant Equations: O level Math

Unless there is a better approach.

An alternative approach:

x=x'
m=m'
So, the area is the triangle on the right, i.e., quarter of the square.

EDIT: x-posted with #2.