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What is the area of each one of those shapes?
OK, let's back up. what is an ALGEBRAIC EXPRESSION for the area of the shape: (use the variable) |dw:1378325478131:dw|
Forget the 5. That's part #2 of the problem. There is no 5 involved here. You are to write a MONOMIAL - that's a single term involving variables, powers and coefficients. Look at the picture. What's an EXPRESSION that gives the area of the shape? It will involve c. It will NOT involve 5.
ok, good... but you can write that with an exponent, right? so the area of ONE of the shapes = \(\Large c^2\)
Then, if that's the area of ONE of them, then what is the combined area of the TWO of them?
ok be c^2*c^2
it be c^4
Noooo..... that would be the PRODUCT of the areas. That doesn't give you the total. If I said, "the square footage of this room is 100 sq. ft, and the square footage of this other room is 150 sq ft", how would you find the TOTAL square footage of BOTH rooms combined?
would you multiply them?? or do something else?
You would multiply, 100x150, to get the total sq area of the 2 rooms?
If the total area is 100x150, then that is =15,000 sq ft. But if you look at the shape and compute the overall area, you'll see that it is: 25x10 = 250 sq. ft. That's a big difference.
You MULTIPLY to get the INDIVIDUAL shape's area, because that's how you compute area. But if you have 2 (or 3 or 7 or 20 ) of the same shape, then you don't multiply all of those total areas to get the overall total area. You ADD them (or, IF they are all the same, then you can multiply the # of shapes x area per shape)
Ok then. The area of one of the shapes = \(\Large c^2\) so what is an expression for the total area of the 2 shapes combined?
How are you getting that? I've already told you, you don't MUTIPLY \(\Large c^2\cdot c^2\). That isnt the correct way to computer the total area, I gave you a counter-example above to convince you. Did you understand that?
not taht good
If the area of one shape is 20 sq inches, and I have 2 identical shapes, then the total area of the 2 shapes combined is: 20 + 20 = 40 OR I could also compute it as: 2 x 20 = 40 Either way works. Think of the rooms in the houses.... the total sq footage of 2 rooms is not the PRODUCTS of each sq. footage, right? It's the SUM of the sq. footages
I never said to subtract the areas. That certainly won't give you the combined total.
im so lost