Just The Right Amount Of Shades

Relevant wiki: Length and Area - Composite Figures

$\large \displaystyle \text{Total area of all the squares} = 5^2 + 4^2 + 3^2 = 25+16+9 = 50\\ \large \displaystyle \text{Area of the not shaded triangle} = \frac{1}{2} \times \text{base} \times \text{height}.\\ \large \displaystyle \implies A = \frac{1}{2} \times 5 \times 12 = 30.\\ \large \displaystyle \text{Area of shaded region} = \text{Total Area} - \text{Not Shaded region} = 50 - 30 = \color{#20A900}{\boxed{20}}.$

Consider the middle square to be a 4×5 rectangle from which a 1 × 4 rectangle is cut. So, the area cut is 1 × 4 = 4. Similarly consider the right square to be a 3 × 5 rectangle from whicn a 2 × 3 rectangle is cut. So, area cut is 2 × 3 = 6.
Now, look at the initial picture which consists of a 5×5 square, 4×5 rectangle and 3×5 rectangle. It looks like a 12 × 5 rectangle. Its diagnol divides it into 2 parts:- upper part and down part. And the rectangles are cut from the upper and shaded part. So, the area of the shaded part is $\text{Area of shaded triangle formed by diagnol (Upper part) - Area of rectangles cut}\\ = \left(\dfrac{1}{2} × 12 × 5\right) - \left(4 + 6\right)\\ = \left(30 - 10\right)\\ = \boxed{20}$ .

$A=\text{Area of the three squares - Area of the triangle}$

$A=5^2+4^2+3^2-\dfrac{1}{2}(5)(12)=$ $\boxed{20}$

60-(30+4+6)=20

area of the black region = area of the three squares - area of the big triangle

area of the three squares = 25 + 16 + 9 = 50 square units

area of the big triangle = 1/2 x 5 x (5+4+3) = 1/2 x 5 x 12 = 30 square units

substitute,

area of black region = 50 - 30 = 20 square units

Relevant wiki: Length and Area Problem Solving

The area of the white portion is 30. It would be area of the dark part, if it were a rectangle with the bottom edge of the shaded part as it's diagonal. From the image we can see that the area of the gap above the middle square is 4. Similarly the area of the gap above the small square is 2*3= 6. So the area of the dark part is 30 - 4 - 6 = 20

Area of the total figure = 25+16+9 sq. units Area of the Unshaded triangle = 0.5x(5+4+3)x5 sq. units $**Area of the Shaded Part = 50-30 =20 sq.units**$