The story of the 7 squares and the red region

The shape can be divided into 2 triangles

$\text{Area} = 162+121.5=\boxed{283.5}$

Sum of areas of the white regions is $\dfrac{1}{2}\times 7\times 9^2=283.5$ .

Hence, the area of the red region is also $\boxed {283.5}$ .

$\text{red area}=\text{area of the 7 squares}-\text{area of the three small unshaded triangles} - \text{area of the big unshaded triangle}$

$\text{red area}=(7 \times 9^2)-3\left(\dfrac{1}{2}\times 9^2\right) - \left(\dfrac{1}{2}\times 9 \times 36\right)=567-121.5-162=\boxed{283.5}$

the area of the red part is exactly the half of the whole so, whole area is 9^2 + 7 = 567 and half of 567 is 288.5