Question 722866: I am trying to assist my son who has a C grade in Ontario Canada Grade 6 Math :(
We were doing just fine until we came across this question and my Googling has gotten me no where.
The question is to determine the length and width of a square with an area of 36 square cm.
The answer is 6 cm each side but how do I teach him a formula to help him?
The same will of course end applying to determining formulas for rectangles, parallelograms and triangles.
Any research so far has the same stuff.
They teach how to determine the area with one unknown or both sides known but not with both unknown.
I feel like a dummy for not being able to help him.
I am 54 years old and I cannot figure this?
Sad it is so I beseech your assistance.
he is a good lad and has shown great marks before.
I fear I have been negligent in not following his progress previously.
He is keen to learn and is excited that I am helping.
He knows I am looking for an answer and is patient.
I thank you for taking the time to help us.
Sincerely
Wm. Makort
Found 2 solutions by josgarithmetic, DrBeeee:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! The question is far too simple for any need for using Google. SQUARE! Length squared is 36.
Let s = length of a side of the square. s*s=36, so what is s? 6*6=36. s=36.
Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! Hello neighbor. My seventh grade advanced math students were in your son's seat last year, so I may be able to help. Let's get right to the issue.
We are calculating the area of a rectangle. Draw a rectangle on the paper - remember all corners are "right" angles (90 degrees), just like the wall. A rectangle has two sets of equal sides, length and width. Now label one side l for length and the other side w for width.
The area is usually designated by the letter A. The formula for the area of a rectangle is
(1) A = l*w, where * means multiply the variable,l, times the variable, w.
Now look at (1). In order to get area, A, we need l and w. This is ALWAYS true, as you found online.
The unique characteristic of a square is the all sides are EQUAL, so l = w. Then we have, for a square with equal sides, s
(2) A = l*w or
(3) A = s*s
So you see, the only reason you need one side for a square is because the length and width are the same number! The square is a special case of a rectangle.
Now to get your son to solve (3) when the area is 36 sqcm, ask him "what number when multiplied by itself equals 36?"
You should have
(4) s*s = 36 or
(5) 6*6 = 36 or
(6) s = 6
You may want to give your son the MSM drill that I give my students to learn all the squares of the counting numbers, 1 to 25. Most know up to 12 from previous grades, but I find it advantageous to know up to 25. MSM means Mad Square Minute.
While we're at it, you may want the area of figures. I recommend Wikipedia.
For area you always multiply two numbers, thus square cm from cm*cm.
Square:
A = s*s
Rectangle:
A = l*w
Parallelogram:
A = b*h, where b is length of the base and h is the perpendicular distance between b and its parallel.
Trapezoid:
A = (1/2)*(b1 + b2)*h, where b1 and b2 are the lengths otf thee parallel sides and h is the perpendicular distance beteen them.
Rhombus:
A = b*h, see parallelogram
PS Live near Buffalo, NY
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