B.
Area:
L•W=area of a rectangle
We can split this shape into three different rectangles. We know that the total width is six, and the mid section of this is two. This means that by default, the width of the other two ends on the "crazy" side are each two.
You now have enough information to begin solving for the area.
2•x
2x units
2•x
2x units
Now, the middle segment is slightly different. It's in one unit less than x, so we should get an equation of:
(x-1)2
2x-2 units
Now we add all the values together
2x+2x+2x-2
2x^3-2 units^2
Perimeter:
2L+2W=perimeter of a rectangle
Now that we have the information of the length and width of each rectangle within the shape, we can solve for the perimeter.
2x+2(2)
2x+4 units
But wait!! We're missing most of one side, the one with the x. This means that instead of the equation I just wrote above, you really should have the one below.
x(x-1)+4
x^2-x+4 units
Since that specific rectangle length and width applies to one of the other rectangles, we won't need to do the math for that one. We just know that it also has a perimeter of x^2-x+4.
Now we just find the perimeter of the middle rectangle.
2(x-1)+2(2)
2x-2+4
2x+2 units
Lastly we add these all together to get the perimeter.
2x+2+x^2-x+4+x^2-x+4
2x^2+8 units
(The 2x, -x, and -x all cancel out)
C.
Area:
πr^2 = area of a circle
Since you have a semicircle, you would put a 1/2 in front of the formula. This will give you the area of the semicircle when you plug in your radius value.
(I am using π to the second decimal)
1/2(3.14)2^2
1/2(3.14)4
6.28 units^2
Now we can find the area of the rectangle. You know that a radius is one half of the diameter, so we can multiply our radius by two to get the length of the rectangle.
2•2
4 units
Next, since we now have the length and width of the rectangle, we multiply them together.
4•x
4x
Lastly, add all the values together to get the total area.
6.28+4x units^2
Perimeter:
2πr = perimeter of a circle
Once again, this is a semicircle, so we have to multiply the formula by one half. Let's plug in our data, too.
[1/2(2)]3.14(2)
1(3.14)2
6.28 units
The perimeter of your semicircle is 6.28.
Now we can find the perimeter of a rectangle.
2L•2W = Perimeter of a rectangle
However, you only have three sides of your rectangle, so this situation would be more like:
1L+2W
Let's plug in our data.
4+2x units
Now the final step is to add the two together.
6.28+4+2x
10.28+2x units
