Answer:
55%
Step-by-step explanation:
Perimeter of a square
[tex]\boxed{P=4s}[/tex]
where s is the side length of the square.
Given the perimeter is 40 cm, substitute this into the formula and solve for s:
[tex]\implies 40=4s[/tex]
[tex]\implies s=10\; \sf cm[/tex]
Therefore, the side length of the square is 10 cm.
Area of a square
[tex]\boxed{A=s^2}[/tex]
where s is the side length of the square.
Therefore, given the side length of the square is 10cm:
[tex]\implies \sf Area\;of\;the\;square=10^2=100\;cm^2[/tex]
Area of a triangle
[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]
where b is the base and h is the height.
The shaded portion of the square is the area of the square minus the sum of the areas of the white triangles.
[tex]\begin{aligned}\textsf{Shaded portion}&=10^2-\left(\dfrac{1}{2}(10-7)(10)+\dfrac{1}{2}(10)(10-4)\right)\\\\&=100-\left(\dfrac{1}{2}(3)(10)+\dfrac{1}{2}(10)(6)\right)\\\\&=100-\left(15+30\right)\\\\&=100-45\\\\&=55\;\sf cm^2\end{aligned}[/tex]
Percent
[tex]\boxed{\sf Percentage=\dfrac{Value}{Total\:value}\right)}[/tex]
To find the percentage of the square that is shaded, divide the area of the shaded portion by the area of the square:
[tex]\begin{aligned}\sf Percentage&=\sf \dfrac{Shaded \;area}{Total\;area}\\\\&=\dfrac{55}{100} \\\\&=0.55\\\\&=55\%\end{aligned}[/tex]
Therefore, the percentage of the square that is shaded is 55%.
