Calculating the Perimeter of Polygons

Professor Dave Explains
25 Oct 201705:07
EducationalLearning
32 Likes 10 Comments

TLDRThe script discusses finding the perimeter of polygons. It explains that perimeter refers to the distance around a shape, so to find perimeter you add up the lengths of all the sides. It provides examples for finding perimeter of rectangles, squares, triangles, and irregular polygons. Formulas are given for perimeter of rectangles and squares. It also demonstrates using algebra to solve for an unknown side length or dimension when given the perimeter. Finally, it notes that finding perimeter of shapes with curvature requires calculus, which is more complex.

Takeaways
  • 😀 Perimeter is the distance around a shape or the boundary enclosing an area
  • 👉 To find the perimeter of a polygon, add up the lengths of all its sides
  • 💡 For a rectangle, perimeter = 2 x (length + width)
  • 💡 For a square, perimeter = 4 x side length
  • 🤔 You can set up equations and use algebra to solve perimeter problems
  • 🔺 For a triangle, again add up all 3 side lengths to get the perimeter
  • 🔺 You can use the Pythagorean theorem if given a right triangle with a missing side length
  • 😕 Irregular shapes take more work - imagine rectangles behind the shape to calculate missing side lengths
  • ❗ Only works for shapes with straight sides - curvature makes perimeter much more complicated
  • 📝 Circles are next - perimeter of circles involves a different concept called circumference
Q & A

  • What does it mean to 'secure the perimeter'?

    -Securing the perimeter means to guard or enclose the boundary of an area so that no one gets in or out.

  • How is the meaning of 'perimeter' in geometry similar to its meaning in movies?

    -In both cases, perimeter refers to the boundary enclosing an area. In geometry specifically, it is the distance around a shape or figure.

  • Why was knowing how to calculate perimeters important for early farmers?

    -Early farmers needed to know perimeter calculations to determine how much material they needed to enclose their land and guard their animals or crops.

  • What is the process for finding the perimeter of a polygon?

    -To find the perimeter of a polygon, add up the lengths of all the sides. This gives the distance around the shape.

  • How can you calculate the perimeter of a rectangle?

    -The perimeter of a rectangle is equal to 2 x (length + width). So multiply the length and width each by 2 and add those numbers.

  • What is the easiest way to calculate the perimeter of a square?

    -For squares, simply take the length of one side and multiply it by 4, since all sides of a square are equal.

  • How can you solve for an unknown dimension in a perimeter word problem?

    -Set up an equation with the given information, then solve for the unknown variable using algebra, often by substitution or elimination.

  • How is finding the perimeter of a triangle different from a rectangle?

    -For triangles, you just add up the three side lengths. For rectangles, you use a perimeter formula based on the length and width.

  • If some side lengths are missing in an irregular polygon, how can you find the perimeter?

    -Look at the other given side lengths to deduce the missing ones. Imagine rectangles behind the shape to calculate missing sides before adding all side lengths.

  • Why does curvature make perimeter calculations more complex?

    -With curved shapes like circles, the perimeter formulas get more complicated. And for non-circular curved shapes, calculus is needed to accurately determine perimeter.

Outlines
00:00
📏 Finding the Perimeter of Polygons

Discusses what perimeter means in geometry, how to calculate the perimeter of various polygons like rectangles, squares, triangles and irregular shapes, using their side lengths. Also covers solving for missing side lengths in perimeter problems using algebra and the Pythagorean theorem.

♾ Introduction to Circles

Mentions that circles have not been covered much yet in the lessons. Transitions to circles being the next topic after checking comprehension on perimeters.

Mindmap
Keywords
💡perimeter
The perimeter is defined in the video as the distance around a shape or figure. It relates to the main theme of finding the perimeters of different polygons. For example, the video shows how to calculate the perimeter of a pentagon by adding up the lengths of all its sides.
💡polygon
A polygon is a shape made up of straight line segments. Finding the perimeters of polygons is the main focus of the video. Different examples of polygons are discussed, like pentagons, rectangles, squares, triangles and irregular polygons.
💡rectangle
Rectangles have two pairs of equal-length sides and four right angles. The video explains that the perimeter of a rectangle can be calculated as 2L + 2W, where L and W are the length and width.
💡square
A square is a special rectangle where all four sides have the same length. The video says that the perimeter of a square can simply be calculated as the side length multiplied by 4.
💡triangle
A triangle is a three-sided polygon. As explained in the video, the perimeter of a triangle is found by adding up the lengths of its three sides. This works even for right triangles with missing side lengths that can be found using the Pythagorean theorem.
💡irregular
An irregular polygon does not have symmetrical sides and angles. The video illustrates how to find the perimeter of irregular polygons by determining unknown side lengths based on other provided side lengths.
💡algebra
Algebra allows unknown values to be represented by variables and solved for using mathematical operations and equations. The video demonstrates solving an algebra perimeter word problem involving a rectangle to find its unknown dimensions.
💡Pythagorean theorem
The Pythagorean theorem is a mathematical equation used to find the length of the hypotenuse (longest side) of a right triangle when the other two side lengths are known. The video shows how this can be used to find a missing side length in order to calculate the perimeter of a triangle.
💡calculus
Calculus is a branch of mathematics used to determine areas, volumes, lengths and other geometric properties of curved figures. The video mentions that calculus would be required to accurately determine the perimeter of shapes with non-circular curvature.
💡circle
Circles are curved shapes where all points are equidistant from the center. While not discussing their perimeters in detail, the video introduces circles as the next geometry topic to cover after polygons.
Highlights

Perimeter is the distance around a shape or figure

Finding the perimeter of a polygon is easy, just add up the lengths of all the sides

Perimeter was an early mathematical necessity for farmers enclosing land

If you walked along each edge and back to start, the distance is the perimeter

Rectangle perimeter is 2 times length plus 2 times width

Square perimeter is 4 times the side length

Can use algebra and equations to solve perimeter problems

Triangle perimeter is sum of 3 side lengths

Can use Pythagorean theorem if missing side length in right triangle

Can figure out missing sides of irregular polygon from other sides

Add up all side lengths to get perimeter of any polygon

Works for shapes with straight sides, not curved boundaries

Circles require calculus to find perimeter

Next we will discuss properties of circles

Understanding perimeters builds towards more advanced mathematics

Transcripts

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