Triangle area and perimeter relationship advice

How to Find Perimeter from Area - Video & Lesson Transcript |

To find the perimeter of the square, add all four sides together. To find the area of a triangle, multiply together two of the sides (not the. Determining the Sides of a Triangle, Given are Perimeter and three Angles Well, the only way that the angles found in the triangle to be in the. Demonstration that a triangle with fixed perimeter does not have a constant area.

The area of a triangle is half of the product of the base and the perpendicular height, so given the base and the area, the height is fixed. But there are only four possible triangles with this height; they are reflections of each other in the axes of the ellipse and so congruent. At the extremes of the subinterval and only there the square root will vanish, leaving y and z equal to each other: Incidentally we have shown that: And for sensible cases There are exactly two isosceles triangles with given perimeter and area.

Going back to the original formula for the relationship between two sides of the triangle x and y for given perimeter p and area A, we can draw this relationship as a set of curves. The chart below looks like a set of contours where p is fixed and A varies between the curves. The scale does not matter. The single point is the case of an equilateral triangle; for a given perimeter the area is maximised.

Triangles with the same area and perimeter

The outer curve again has the same perimeter and with two-thirds of the maximum area. The triangle has the same perimeter, but deals with the case where the area is zero; no side can exceed half the perimeter but one of them must be equal to half the perimeter. Take the inner curve for example, which was based on a perimeter of 98 and area of Choosing a particular value for x for the length of one of the sides enables two possible values for y to be read off the chart — one of these can taken as the second side and the other the third.

But similarly a particular value of y allows two values of x to be read of the chart.

Triangles with the same area and perimeter

But there is even more symmetry involved. Recalling the 25,34,39 Heronian triangle, not only do the points 25,34 and 25,39 lie on the curve, but so do 34,25 and 39,25 and also 34,39 and 39, We also know some other points on this curve: Now, given that, what is the area of this figure?

Well, the area's going to be 12 units times 5 units to get 60 square units. Area is equal to So this one right over here has the same area, different perimeter. Same area as the original yellow rectangle, different area. Now let's go over here. So this is not just a rectangle.

Solve Right Triangle Given Perimeter and Area - Problem With Solution

This is also a square, because I have the same length and the same width. So what's the area here? Well, for the area, I just have to multiply the length times the width. And what is the perimeter here? Well, these two sides are going to make up half the perimeter. If I wanted to figure out the whole one, I know this is also 8 and this is also 8. So the perimeter is 8 times 4. So this square right over here has a different area, but it has the same perimeter as our original yellow square.

Now let's move onto this blue one. And you're probably getting used to this. And what's the perimeter? Well, it's going to be 4 plus 15, and whatever that is times 2. And then 19 times 2 is So this one right here has the same area, different perimeter as our original. Now, finally, here in purple, what is the area? The area is 10 times 20, which is equal to So if it's 10, say, well, 10 units times 20 units is square units. And what is the perimeter?

What is the perimeter? Well, 10 plus 20 is 30, but I've just considered only two of the sides right here. That's only half way around. So 10 plus 20 is 30 times 2 is This has a different area, and it also has a different perimeter.

Area and Perimeter of Triangles ( Read ) | Geometry | CK Foundation

This one's perimeter looks just like the same number. It's 60, as is the area here, but that's not what we're comparing. We have a different perimeter and different area. So neither of these are the same as our original rectangle.