Answer:
55%
Step-by-step explanation:
Since each side of a square is the same, let's say it's x. The perimeter is just 4x, but we also know its numerical value is 40. We set these equal to find x:
4x = 40
x = 10
Now that we know x is 10, we can figure out the rest of the problem.
First, draw a diagonal from the top right corner of the square to the bottom left corner. This splits the shaded region into two triangles. Let's look at the leftmost triangle:
We see that its base is 7. We also know its height: its height is simply the side length of the square, which is 10. So, using the formula for a triangle area, bh/2, we get: (7)*(10)/2 = 70/2 = 35 cm squared.
Now, we calculate the area of the second triangle. Its base is 4, and its height is also the side length of the square, 10. So: 4 * 10 / 2 = 40/2 = 20 cm squared.
Adding these two areas, we get the total shaded area: 35 + 20 = 55 cm squared.
The total area of the square is: 10 * 10 = 100.
To find the percentage of the area shaded, we simply divide the shaded area by the total square area: 55/100 = 55%, and that's our answer.
