Use the formula for the area of the triangle Area=b*h/2.
If the base becomes b'=2b and h'=h/2, then the area of this new triangle is Area'= (2b)*(h/2)/2.
As you can see the two 2's introduced cancel one another and the area is unchanged. A'=A.
If the base is doubled and the height remains the same, then b''=2b, and
h''=h. Substitute in the area formula for a triangle to get
A''=b''*h''/2= (2b)*h/2= 2*(b*h/2)=2A
You see that in this case the area is doubled.
Use the formula for the area of the triangle with symbols.
Let b be the measure of the base, and h the measure of the height.
The area of the triangle is A= b*h/2 (original situation)
Now consider the new situation (situation2)
Let b` the new base and h`the new height.
We have b'=2b, and h`=h/2
The new area A`=b`*h`/2=(2b)*(h/2)/2=b*h/2 and that is equal to the original situation.
Now consider a third situation
Let b"=2b, h"=h
A"=b"*h"/2=(2b)*h/2=2(b*h/2)=2A
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