Perimeter And Area With Polynomials

Learning Outcomes

Write polynomials involving perimeter, expanse, and book

In this section we will explore ways that polynomials are used in applications of perimeter, area, and book. First, we will encounter how a polynomial tin exist used to describe the perimeter of a rectangle.

Example

A rectangular garden has one side with a length of [latex]x+7[/latex] and another with a length [latex]2x + 3[/latex]. Discover the perimeter of the garden.

Try Information technology

In the post-obit video you are shown how to detect the perimeter of a triangle whose sides are defined as polynomials.

The area of a circumvolve tin can be found using the radius of the circumvolve and the constant pi in the formula [latex]A=\pi{r^2}[/latex]. In the adjacent example nosotros volition utilize this formula to find a polynomial that describes the area of an irregular shape.

Case

Find a polynomial for the area of the shaded region of the figure.

circle with middle extracted to form a ring shape. Inner radius labeled as r=3, outer radius labeled as R= r.

In the video that follows, you will be shown an example of determining the area of a rectangle whose sides are divers equally polynomials.

A note about pi.

It is easy to confuse pi as a variable because we use a greek letter of the alphabet to correspond it. We use a greek letter instead of a number considering nobody has been able to find an end to the number of digits of pi. To be precise and thorough, we use the greek letter every bit a way to say: "we are including all the digits of pi without having to write them". The expression for the area of the shaded region in the example higher up included both the variable r, which represented an unknown radius and the number pi. If we needed to employ this expression to build a concrete object or instruct a auto to cutting specific dimensions, nosotros would round pi to an appropriate number of decimal places.

In the next example, we will write the area for a rectangle in two unlike ways, one as the product of two binomials and the other as the sum of 4 rectangles. Considering we are describing the same shape two different ways, nosotros should end up with the same expression no matter what fashion we ascertain the area.

Case

Write 2 dissimilar polynomials that describe the surface area of of the figure. For one expression, recollect of the rectangle as one large figure, and for the other expression, think of the rectangle as the sum of [latex]four[/latex] different rectangles.

Rectangle with side length y+9 and y+7

The last example we will provide in this section is 1 for volume. The volume of regular solids such every bit spheres, cylinders, cones and rectangular prisms are known. We will find an expression for the volume of a cylinder, which is defined equally [latex]V=\pi{r^2}h[/latex].

Example

Define a polynomial that describes the book of the cylinder shown in the effigy:

Cylinder with height = 7 and radius = (t-2)

In this last video, nosotros present some other example of finding the volume of a cylinder whose dimensions include polynomials.

In this department nosotros defined polynomials that represent perimeter, area and book of well-known shapes. We likewise introduced some convention nearly how to utilize and write [latex]\pi[/latex] when information technology is combined with other constants and variables. The side by side application will introduce you lot to cost and revenue polynomials. Side by side we will run into that price and revenue equations tin can be polynomials.

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