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As Report cards are coming out in a few weeks, remember the POTW can be related to many things outside of math (like Responsibility and Initiative, even Collaboration).
Grade 7/8 POTW We may not know any values such as the length & width of the rectangle, base & height of any triangles, etc, but we do know the equal lengths as well as the area of one triangle. This is enough to solve for the area of the larger rectangle. First, let’s give simpler variables for the values instead of PC, CQ, etc. For QA = AB = BR, we can give it a value of x, while for PC = CQ, we can give it a value of y. In other words: QA = AB = BR = x PC = CQ = y Now, we can calculate for the entire rectangle using these values: PQRS = ACS + ACQ + ARS + CPS 3x2y = 10 + ((xy)/2) + ((2x2y)/2) + ((3xy)/2) 6xy = 10 + 0.5xy + 2xy + 1.5xy 6xy = 10 + 4xy 6xy - 4xy = 10 + 4xy - 4xy 2xy = 10 2xy/2 = 10/2 xy = 5 Although we don’t have the value of x and y separately, we don’t actually need it. We still can’t calculate the rectangle on its own, but we can solve for the shapes separately and add (similar to above). PQRS = ACS + ACQ + ARS + CPS PQRS = 10 + ((xy)/2) + ((2x2y)/2) + ((3xy)/2) PQRS = 10 + 5/2 + (2)(2)(5)/2 + 3(5)/2) PQRS = 10 + 2.5 + 10 + 7.5 PQRS = 30cm^2 Therefore, rectangle PQRS has an area of 30cm^2.
I did my POTW on paper. My answer was 30 cm2. The way I did it was: I used variables to represent the missing values, and used the variables to represent the way to find the area of each separate triangle, and adding it together to get the final product.
Grade 7/8 POTW
ReplyDeleteWe may not know any values such as the length & width of the rectangle, base & height of any triangles, etc, but we do know the equal lengths as well as the area of one triangle. This is enough to solve for the area of the larger rectangle.
First, let’s give simpler variables for the values instead of PC, CQ, etc. For QA = AB = BR, we can give it a value of x, while for PC = CQ, we can give it a value of y. In other words:
QA = AB = BR = x
PC = CQ = y
Now, we can calculate for the entire rectangle using these values:
PQRS = ACS + ACQ + ARS + CPS
3x2y = 10 + ((xy)/2) + ((2x2y)/2) + ((3xy)/2)
6xy = 10 + 0.5xy + 2xy + 1.5xy
6xy = 10 + 4xy
6xy - 4xy = 10 + 4xy - 4xy
2xy = 10
2xy/2 = 10/2
xy = 5
Although we don’t have the value of x and y separately, we don’t actually need it. We still can’t calculate the rectangle on its own, but we can solve for the shapes separately and add (similar to above).
PQRS = ACS + ACQ + ARS + CPS
PQRS = 10 + ((xy)/2) + ((2x2y)/2) + ((3xy)/2)
PQRS = 10 + 5/2 + (2)(2)(5)/2 + 3(5)/2)
PQRS = 10 + 2.5 + 10 + 7.5
PQRS = 30cm^2
Therefore, rectangle PQRS has an area of 30cm^2.
Grade 7/8 POTW:
ReplyDeleteInstead of having actual value for the length and width of PSQR, we do have variables that we can use for these values.
PC = CQ = x
QA = AB = BR = y
Now, we can use these values and try to find the area of PSQR.
PSQR = PCS + CAS + CQA + ARS
3y2x = (x3y/2) + (10) + (xy/2) + (2y2x/2)
3y2x = (3xy/2) + 10 + (xy/2) + (2yx)
6yx = 1.5xy + 10 + 0.5xy + 2yx
2yx = 10
yx = 5
Since we don’t need the individual values for y and x (each variable in the equation requires an xy), we can plug 5 into the equation.
PSQR = (x3y/2) + (10) + (xy/2) + (2y2x/2)
PSQR = (3*5/2) + (10) + (5/2) + (2*5*2/2)
PSQR = (7.5) + (10) + (2.5) + (10)
PSQR = 10 + 10 + 10
PSQR = 30
Rectangle PSQR has an area of 30 cm^2.
POTW:
ReplyDeleteI did my POTW on paper. My answer was 30 cm2.
The way I did it was: I used variables to represent the missing values, and used the variables to represent the way to find the area of each separate triangle, and adding it together to get the final product.