Hey guys! Welcome to this video on finding the area and perimeter of an object.
The area and perimeter help us to measure two dimensional shapes.
The area measures the surface of an object, and the perimeter measures the length of the
outside of an object. For instance, let's say you have a rectangular pool
and you want to find a tarp to cover it, then you would need to know the area of the surface of the pool.
But, if you wanted to know the distance it would take for you to walk around
the pool, then you would need to know the perimeter of the pool's surface.
So now, let's take a look at how to calculate each.
First, perimeter. To calculate the perimeter of any polygon you just add up the length of all the sides.
Let's use our rectangular pool as an example.
Let's say that the width is 15ft,
and the length is 7ft.
Since, it is a rectangle we
know that the parallel sides have the same length.
So we have all the information we need, now we just add up all the sides.
Let's start with our formula. Let's say 15
is equal to 'a,' and 7 is equal to b. So we have Perimeter= a + a + b + b.
Now let's plug in our numbers. Perimeter = 15ft + 15ft + 7ft + 7ft, and when we add it all
up we get the Perimeter is equal to 44ft.
We can even simplify our Perimeter formula
for a rectangle. Since we know that there are 4 sides, and that there are two sets of
identical sides (you know, the two sides that are parallel to each other) we can then simplify
our formula to Perimeter = 2(a+b). Let's try it, and see if we get the same thing.
Perimeter = 2 (15ft+7ft)= 2(22ft)=44ft
So, you can see here that we do indeed get the same thing.
We can apply this same sort of principle to finding the perimeter of a square.
Since, a square has four sides that are the same
measurement, we can say that the Perimeter of a square is equal to 4 x a.
Same principle with an equilateral triangle. All three sides are the same so we can say Perimeter = 3 x a.
An Isosceles triangle has two sides that are the same so we can
write our perimeter formula as Perimeter = 2a +b.
Now, the only shape whose perimeter may seem a little less obvious to find is our friend the circle.
You guys may have heard of the term circumference.
Well the circumference is the exact same thing as the perimeter of a circle...
*some mathematicians may get a little on edge about which term you use... Because technically
perimeter is defined as "the sum of the lengths of the edges of a closed figure,'.....
and a circle doesn't have edges....
But the definition for circumference is the perimeter of a circle...
So, whichever you prefer to call it let's look at how you find it.
To find the circumference of a circle
you multiply the diameter of the circle times pi.
Alright, now on to area. When we were looking at the perimeter of different shapes
we were able simplify the formulas. Giving us different formulas for different shapes,
yet keeping in line with the definition of adding up all the sides.
Well, similarly, when finding the area of an object the formula will be different for
different shapes, but each formula represents a solution to solving for the area of the object's surface.
So, let's take a look at the different shapes,
and the area formula corresponding to each shape.
- First, we have the parallelogram. The area of a parallelogram is equal to width x height.
- The area for a triangle is equal to 1/2 b x h
- The area for a trapezoid is equal to 1/2 (a + b) x h
- The area of an Ellipse is equal to pie x a x b
And - The area of a circle is equal to pi x r^2
Okay, now let's look at some examples of how to solve for the area of an ellipse, and the
area of a trapezoid.
Let's say we have an ellipse
that intersects the y-axis at 4, and intersects on the x-axis
at 6. 'A' is our length along the y-axis, and 'b' is our length along the x- axis. So, we have a=4, and b=6.
Now, let's plug in our numbers into the formula for an ellipse.
Area= pi x 4 x 6 = 75.36units^2
Now let's say you have a trapezoid.
We'll say that our height is equal to 7,
our "A" side is equal to 8,
and our "B" side is equal to 5.
So now we do the exact same thing we
did last time. We just plug in our numbers into our formula for area
A= 1/2(8 + 5) * 7
A= 7(7) A= 49 units^2
Alright guys, I hope that this video has been helpful. If you guys enjoyed it, hit the like
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