The perimeter of a quadrilateral

Seamus needs a fence around his pasture. He intends to use chicken net for the fence. How many meters of chicken net does he need to buy? To find out, he could measure around the entire garden. But in this case he doesn't have to.

The pasture Has four sides.. ..and four corners, so it is a.. ..quadrangle. These two sides have a common corner. These two sides have a common corner. These two sides have a common corner. And this corner is common to these two sides.

But these two sides do not have a common corner: they are opposite sides. And so are these two. And the angles in all the corners are ninety degrees: they are right angles. Which means that these opposite sides are the same length as each other. And these opposite sides are the same length as each other.

And the shape of the pasture is a rectangle. When the pasture is rectangular, Seamus only needs to measure two sides: Two sides that have a common corner. For example these two. He measures one side as 30 meters, and the other as 10 meters. The border of the pasture, the perimeter around it, is then: 30 plus 10 plus 30 plus 10 meters.

That is equal to 80 meters. He needs to buy at least 80 meters of chicken net. This is a boxing ring. All sides are five meters long. ..and all angles are ninety degrees .. It’s a square.

To calculate how many meters of rope are needed around the boxing ring .. ..we add the four sides: 5 plus 5 plus 5 plus 5, equals 20 meters. Or we multiply 5 by four. That is also 20 meters. If you lean the sides of a square, like this: Then the angles are no longer ninety degrees. So it is not a square, but a.. ..rhombus.

The perimeter of a rhombus is calculated in the same way as for the square. We can extend the sides of a square, a rectangle, or a rhombus. But however far we extend the opposites sides, they never cross each other. The opposite sides are parallel. These figures are therefore various kinds of parallelogram.

All parallelograms have opposite sides that are equally long. To calculate the perimeter of a parallelogram, we therefore only need to measure two sides that have a common corner. A figure that has only two sides that are parallel.. ..is called a trapezoid. If there are two opposite sides of a trapezoid.. ..that are equally long, then it is an.. ..isosceles trapezoid. We can show that the sides are equally long with a mark: a little line, on the two sides.

If the two equally long sides are both 5 meters, and the other two sides are 3 meters and 7 meters, then the perimeter is: 5 plus 5 plus 3 plus 7 meters. That’s 20 meters. But if none of the four sides are the same length as any other, then we do have to measure all of the sides to calculate the perimeter. - And that’s that!