ABCBD IS A SQUARE AND EFGH IS A PARALLELOGRAM. ED IS EQUAL TO DH .FIND THE SHADED AREA OF THE FIGURE
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
Second, it would help if you proofread your questions before you posted them.
"ABCBD" is a square?
Lastly, we have no idea what is shaded in your figures.
To find the shaded area of the figure, we need to determine the areas of the square ABCD and the parallelogram EFGH separately, and then subtract the area of the smaller shape from the larger one.
Given that ABCD is a square and EFGH is a parallelogram, let's address each shape individually.
1. Area of Square ABCD:
Since all the sides of a square are equal, we only need to know the length of one side to determine the area. Let's assume the side length of ABCD is 's'.
The area of a square is given by the formula: Area = side length^2. Therefore, the area of ABCD is s^2.
2. Area of Parallelogram EFGH:
To find the area of a parallelogram, we need the base length and the height. However, in this case, we are not given the height of EFGH directly.
Given that ED and DH are equal, we can infer that EH is also equal in length. This means the height of the parallelogram (EH) is equal to the side length of ABCD (s).
Now, to find the base length, we need to look at EH in relation to the side length of the square. From the diagram, we can see that EH is parallel to AB (which is equal to s) and BD. Therefore, the base length of EFGH is equal to BD, which is twice the value of the side length (2s).
So, the area of EFGH is calculated using the formula: Area = base length * height = (2s) * s = 2s^2.
Now that we have calculated the areas of both shapes, we can find the shaded area by subtracting the area of the square from the area of the parallelogram:
Shaded Area = Area of EFGH - Area of ABCD
Shaded Area = (2s^2) - (s^2)
Shaded Area = s^2.
Hence, the shaded area of the figure is equal to the square of the side length (s).