For Part "A":
First, we know that the shape is made up of rectangles (as I say, longer squares). To find the area of a square, we need to multiply one side by the another side, but we are not dealing with equal sides.
To find the area of a rectangle you do the same thing, except you don't have equal lengths.
We see the "shape" is made up of TWO rectangles, so to find the area of the full shape, we add the areas together.
As so:
The first rectangle's lengths are 7 and X (and 7 and X again; since the opposite side of a rectangle are equal. )
So, the area of this rectangle is:
L x W
(length x width)
So...
7 x X = 7x
(We don't know what X is, so we have to leave the equation as is.)
The second rectangle has sides of 6 and X (6 and X again).
L(ength) x W(idth) = A(rea)
6 x X = 6x
Now, we have the two areas (simplified as much as possible) 6x & 7x.
To write an expression of the area of the polygon,
we need to add those two areas together.
As so:
[Rectangle1's (L x W) + Rectangle2's (L x W) = Area of entire polygon.] <- This could be your expression/answer if that is what you are looking for in part A.
(6 x X) + (7 x X) =
(6x) + (7x) = 13x
For part B:
Since we know that the area of both of the rectangles is 13x, we can use this information to find the value of X by setting up a simple equation like this:
13x = area of polygon
13x = 65
Well, this can be simplified too easily!
As following:
13x = 65
(We need to get X by itself to find its value. We do this by dividing 13, from X, on both sides.)
13x / 13 = 65 / 13
x = 5.
For part C...
replace x for 5 on each rectangle and label all of the sides that are missing.
Hope I could help you out! I apologize for taking so long for this answer. If my math is wrong, or I provided an answer you were not looking for, please let me know! However, if my math was well-explained, please consider marking my answer Brainliest! :)
Have a good one.
God bless!
