Will a triangle and a Parallelogram with the same Perimeter have the same area?

Question

bh/2 = area of a triangle bh = area of Parallelogram

Answer 1

not all parallelograms with the same perimeter will have the same area. for example:

a rectangle that is 4 x 6 would have an area of 24 and a perimeter of 20

another rectangle that is 2 x 8 would also have a perimeter of 20, but an area of 16.

Since this is a case, the triangles will, in most cases, not have the same area as a rectangle.

Answer 2

Not necessarily, and all I have to do is give a counterexample.

Let's take a right angle triangle with the measurements 3,4,5. That is, 3 is the base, 4 is the height, and 5 is the hypotenuse. The perimeter of this triangle is 12.

Now, let's take a rectangle (which are parallelograms with 90 degree angles) with length 5 and width 1. The perimeter is 5+1+5+1 = 12.

However, the area of the triangle is (1/2)(3)(4) = 6, and the area of the rectangle is 5 x 1 = 5.

Thus, this is one example where they don't have the same area, so it is not a true statement.

Answer 3

No, I'll show you by example.

Say you have a 3,4,5 right triangle and a square with sides 3 (Note that a square is a type of parallelogram). Both have a perimeter of 12 units. The triangle will have an area of 6 square units, while the square has an area of 9 square units.

6 does not equal 9, so they have the same perimeter, but not the same area.

Answer 4

you can picture the parallelogram stretched out to approach a width of 1/2 of the perimeter. As this happens, the area will shrink to 0. So two parallelograms with the same perimeter do not have necessarily have the same area.

The same can be said about the triangle, for the same reason.

Now I think you can answer the question yourself.

Answer 5

You can't just define a parallelogram by its perimeter - if you make it very very thin, you can get its area as close to 0 as you want; if you make it a square, you'll get a big area. So there are lots of different areas of a parallelogram with a given perimeter (and the same applies to triangles). You'll need to adjust your question a little

Answer 6

no