Answer:
55%.
Step-by-step explanation:
Since we know that all sides of a square have equal length and perimeter of a square is 4 times the length of one side of square, so we can find length of each side of square by multiplying 40 by 4.
[tex]\text{Each side length of square}=\frac{40}{4} =10[/tex]
Now we will find the area of our square with side length 10.
[tex]\text{Area of square}=\text{(10 cm)}^{2}=100\text{ cm}^{2}[/tex]
Now we will find the area of shaded region by subtracting the non-shaded area of square from the total area of square. We can see that non-shaded part of our square is in form of two right triangle.
Let us find area of triangle whose base is 10 cm and height is 6 cm (10-4).
[tex]\text{Area of horizontal base triangle}=\frac{1}{2}\cdot 10\cdot 6[/tex]
[tex]\text{Area of horizontal base triangle}=5\cdot 6=30[/tex]
Now let us find area of triangle whose base is 10 cm (vertical) and height is 3 cm (10-7).
[tex]\text{Area of horizontal base triangle}=\frac{1}{2}\cdot 10\cdot 3[/tex]
[tex]\text{Area of horizontal base triangle}=5\cdot 3=15[/tex]
Now let us find area of shaded part inside square by subtracting area of two triangles from area of square.
[tex]\text{Area of shaded part inside square}=100-(30+15)[/tex]
[tex]\text{Area of shaded part inside square}=100-(45)[/tex]
[tex]\text{Area of shaded part inside square}=55[/tex]
Therefore, area of shaded part inside square is [tex]55 cm^{2}[/tex]
Now let us find 55 is what percent of 100.
[tex]\text{Percentage of shaded area inside square}=\frac{55}{100} \cdot 100[/tex]
[tex]\text{Percentage of shaded area inside square}=55[/tex]
Therefore, 55% of the area inside the square is shaded.
