Area In Mathematics Full Explanation

The area in mathematics terms is defined as a two-dimensional space captured by an object. The use of the area of Note Study.com has many practical applications in building, agriculture, architecture, and science. You need to add and even cover how much carpet you’ll have in your homeroom.

Area In Mathematics
Area In Mathematics

Sometimes the area is very easy to determine. For a square or rectangle, the area is the number of square units inside the shape and says “Brain Quest Grade 4 Workbook.” Such polygons have four sides and are width multiplied by length to the area.

Can be asked. However, finding the area of ​​a circle, or as a triangle becomes more complex, can include the use of various formulas.

True Area, why it was invented, it is convenient to look at the history of mathematical concepts in life, but also understand the notions that are important in business, scholars, and everyday life.

History and examples

Some of the first known works on the area came from Mesopotamia, Mark Ryan states in “Dummy, Geometry for the Second Edition.” Also teaches a workshop for parents. Has authored numerous math books.

This high school math teacher says to develop concepts for dealing with areas of Mesopotamia, fields, and properties:
“Farmers know that if one farmer planted twice as wide and three times as long and area as the other, then a large plot would be 3×2 or 6 times as one smaller. Was. “

The concept of the area had many practical applications in the last few centuries in the ancient world of Ryan Note:

  • The architect of the Giza Pyramid, who was built about 2,500 BC, was great to know how to make the sides of each triangle in a structure using a formula for finding the area of ​​a two-dimensional triangle.
  • The Chinese knew how to calculate the area of ​​many different 2D shapes by about 100 BC.
  • Johannes Kepler measured the area of ​​the section of the orbit of the planet, which lived from 1571 to 1630, as they circled the day using formulas for calculating the area of ​​ellipses and circles.
  • Calculations that use the concept of territory developed by Sir Isaac Newton.

So, ancient humans, and even those who lived through, had many practical uses for the age of reason, the concept of the region.

A simple formula was developed to find areas of various 2D shapes, once the concept has become even more convenient in practical applications.

Formula to determine the area

Before looking at practical uses for the concept of regions, we first need to know the formulas for finding areas of various shapes. Fortunately, the polygonal ones, including these most common ones, determine the area where there are many formulas used for :

Rectangle

A rectangle is a special type of rectangle where all internal angles are equal to 90 ° and all sides are the same length. The formula for finding the area of ​​a rectangle:

XW = H

“A” represents the area, “H” is the height and width “W”.

square

A square is a special type of rectangle whose sides are equal. Therefore, the formula for finding a square is easier than the one for finding a rectangle.

A = SXS

Here, “A” means the area, and “S” means the length of one side. Since all sides of the square are equal, you simply multiply the two sides to find the area. (In more advanced mathematics, the formula is written as A = S ^ 2, or the area is equal to the side power.)

triangle

A triangle is a figure with three sides closed. The vertical distance from the base to the opposite highest point is called the height (H). So the formula looks like this:

A = ½X B, XH

As mentioned, “A” is the base of the triangle, and “H” is the height when it represents a region.

Circle

Area A circle is the total area that is limited by the circumference or the distance on the circumference. You draw the perimeter and think of the area of ​​the circle as if it were filled with an area within the circle of paint or crayon. The formula for the area of ​​a circle is:

A = πXR ^ 2

In this equation, “A” again represents the radius of the region, “R” (half the distance from one side of the other circle), π is 3.14, pronounced “PI” Greece It is a letter (the ratio of the circumference of a circle to its diameter).

Practical application

You need to calculate the area of ​​various shapes and there are many real and real reasons. For example, suppose you are looking for your lawn for SOD. You need to know enough about your lawn area to buy enough turf. Or you may want to carpet your living room, hall, or bedroom.

Again, you need to calculate the area to determine how much carpet to buy for the various sizes of your room. Knowing the formula that calculates the area will help you determine the area of ​​the room.

If your living room is 18 feet to 14 feet and you want to search for an area so that you can buy the correct amount of carpet, for example, you will find a rectangular area: Use the formula for.

XW = H
A = 14ft x 18ft
= 252 square feet A.

So you need 252 square feet of carpet. In contrast, if you want to lay tiles for your bathroom floor, which is circular, measure the distance from one side of the circle that divides it with the other diameter by the following two. Then you apply the formula to find the area of ​​a circle as follows:

= π (1/2 XD) ^ 2

Where “D” is the diameter, as mentioned above, the other variable. If your circular floor is 4 feet in diameter, you need:

= π × (1/2 XD) ^ 2
= π × (1/2 × 4 feet) ^ 2
A = 3.14 X (2 feet) ^ 2
A = 3.14 x 4 feet
A = 12.56 square feet

You will be off to that number around 12.6 sq ft or 13 sq ft. So you will need 13 square feet of tiles to complete your bathroom floor.

If you have a room that looks really good in the shape of a triangle, and you want to carpet that room, use the formula for finding the area of ​​a triangle. I think you need to measure the base of the first triangle. Suppose you find the base to be 10 feet.

You want to measure the height of the triangle from the top base of the point of the triangle. If the floor height of your triangular room is 8 feet, you would like to use the formula as follows:

A = ½X B, XH
A = ½ x 10 feet x 8 feet
A = ½X 80ft
A = 40 square feet

So you would need a whopping 40 square feet of carpet to cover the floor of the room. Make sure you have enough credit left on your card before heading to a home improvement or carpet store.

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