Determining the perimeter and area of \u200b\u200bgeometric shapes is an important task that arises when solving many practical or everyday problems. If you need to glue the wallpaper, install a fence, calculate the consumption of paint or tiles, then you will definitely have to deal with geometric calculations.
To solve the listed everyday issues, you will need to work with a variety of geometric shapes. We present to you a catalog of online calculators that allow you to calculate the parameters of the most popular flat figures. Let's consider them.
A circle
Special cases
A rectangle with the same sides. A parallelogram becomes a rhombus if its diagonals intersect at an angle of 90 degrees and are bisectors of their angles.
It is a parallelogram with right angles. In addition, a parallelogram is considered a rectangle if its sides and diagonals meet the conditions of the Pythagorean theorem.
This is a parallelogram in which all sides are equal and all angles are equal. The diagonals of the square completely repeat the properties of the diagonals of the rectangle and the rhombus, which makes the square a unique shape that is characterized by maximum symmetry.
Polygon
A regular polygon is a convex shape on a plane that has equal sides and angles. Depending on the number of sides, polygons have their own names:
- - the pentagon;
- - hexagon;
- eight - octagon;
- twelve is the dodecagon.
Etc. Geometers joke that a circle is a polygon with an infinite number of angles. Our calculator is programmed to determine the perimeters and areas of regular polygons only. It uses general formulas for all correct polygons. To calculate the perimeter, use the formula:
where n is the number of sides of the polygon, a is the length of the side.
To determine the area, the expression is used:
S \u003d n / 4 × a 2 × ctg (pi / n).
Substituting the corresponding n, we can find a formula for any regular polygon, which also includes an equilateral triangle and a square.
Polygons are very common in real life. So the building of the US Department of Defense - the Pentagon - has the shape of a pentagon, a hexagon - honeycombs or snowflake crystals, an octagon - road signs. In addition, many protozoa, such as radiolarians, have the shape of regular polygons.
Real life examples
Let's take a look at a couple of examples of using our calculator in real calculations.
Fence painting
Painting surfaces and calculating paint are some of the most obvious everyday tasks that require minimal mathematical calculations. If we need to paint a fence that is 1.5 meters high and 20 meters long, how many cans of paint are required? To do this, you need to find out the total area of \u200b\u200bthe fence and the consumption of paints and varnishes per 1 square meter. We know that enamel consumption is 130 grams per meter. Now let's determine the area of \u200b\u200bthe fence using the rectangle area calculator. It will be S \u003d 30 square meters. Naturally, we will paint the fence on both sides, so the area for painting will increase to 60 squares. Then we need 60 × 0.13 \u003d 7.8 kilograms of paint or three standard cans of 2.8 kilograms.
Fringed trim
Clothing tailoring is another industry that requires extensive geometric knowledge. Suppose we need to trim a scarf with a fringe, which is an isosceles trapezoid with sides of 150, 100, 75 and 75 cm. To calculate the fringe consumption, we need to know the perimeter of the trapezoid. This is where the online calculator comes in handy. Let's enter this cell data and get the answer:
Thus, we need 4 m of fringe to trim the scarf.
Conclusion
Flat figures make up the real world around. We often wondered at school, will geometry be useful to us in the future? The above examples show that mathematics is constantly used in everyday life. And if the area of \u200b\u200ba rectangle is familiar to us, then calculating the area of \u200b\u200ba dodecagon can be difficult. Use our catalog of calculators to solve school assignments or everyday issues.
How to calculate the area of \u200b\u200ba figure knowing its perimeter? and got the best answer
Answer from Yeemen Arkadievich [guru]
In Compass 3D, plot a plan and automatically calculate the area. The area of \u200b\u200ban arbitrary polygon cannot be calculated along the perimeter. You still have to break it down into separate shapes.
If you have any questions, write to the agent.
Answer from Kamis Sh[newbie]
..
Answer from Kiss (RUSS for all) ki (i)[guru]
1.select center
2.measure the distance from center to corners
3.measure the sides of your polygon
4. calculate the perimeters of the resulting N triangles
5. Calculate the areas of all triangles using Heron's formula - through a semi-perimeter.
6.Sum up all areas
7.Choose my answer as the best one.
8.all
Answer from Semrid[guru]
try dividing the perimeter by 4 and then multiplying it by each other
Answer from ScrAll[guru]
Cut out of paper and weigh.
Or you break it into triangles.
Half base to height ...
Answer from Alexey Zaitsev[guru]
It is easier and more accurate to draw a sketch - a top view with dimensions. Then, according to this sketch, divide the area into rectangles, calculate and sum up their areas
Answer from Maria Kempel[active]
unrealistic
Answer from Nemo[guru]
Unrealistic. The area of \u200b\u200bonly RIGHT figures is calculated along the perimeter. I advise in a piecewise way
Answer from Djon[guru]
it is best to break a complex figure into several simple ones, and calculate the area separately, then add
Answer from Lavavoth[guru]
Unrealistic.. . Better lay out the floor plan, there are other ways of counting, but you need to see the plan.
Answer from 3 answers[guru]
Hello! Here is a selection of topics with answers to your question: How to calculate the area of \u200b\u200ba figure knowing its perimeter?
Petya wants to draw a figure with a perimeter of 12 cm and an area of \u200b\u200b12 sq. see Prove He Can't Do It
the maximum area around the perimeter of the figure is the Circle.
If the area of \u200b\u200ba circle with a long circle is 12
When solving, it is necessary to take into account that to solve the problem of finding the area of \u200b\u200ba rectangle only from the length of its sides can't.
This is easy to verify. Let the perimeter of the rectangle be 20 cm. This will be true if its sides are 1 and 9, 2 and 8, 3 and 7 cm. All these three rectangles will have the same perimeter equal to twenty centimeters. (1 + 9) * 2 \u003d 20 just like (2 + 8) * 2 \u003d 20 cm.
As you can see, we can pick up endless number of options the sizes of the sides of the rectangle, the perimeter of which will be equal to the specified value.
The area of \u200b\u200brectangles with a given perimeter of 20 cm, but with different sides, will be different. For the given example - 9, 16 and 21 square centimeters, respectively.
S 1 \u003d 1 * 9 \u003d 9 cm 2
S 2 \u003d 2 * 8 \u003d 16 cm 2
S 3 \u003d 3 * 7 \u003d 21 cm 2
As you can see, there are an infinite number of options for the area of \u200b\u200ba figure for a given perimeter.
Thus, in order to calculate the area of \u200b\u200ba rectangle from its perimeter, it is necessary to know either the aspect ratio or the length of one of them. The only figure that has an unambiguous dependence of its area on the perimeter is the circle. For circle only and a solution is possible.
In this tutorial:
- Task 4. Changing the length of the sides while maintaining the area of \u200b\u200bthe rectangle
Problem 1. Find the sides of a rectangle from the area
The perimeter of the rectangle is 32 centimeters, and the sum of the areas of the squares built on each of its sides is 260 square centimeters. Find the sides of the rectangle.Decision.
2 (x + y) \u003d 32
According to the condition of the problem, the sum of the areas of the squares built on each of its sides (squares, respectively, four) will be equal to
2x 2 + 2y 2 \u003d 260
x + y \u003d 16
x \u003d 16-y
2 (16-y) 2 + 2y 2 \u003d 260
2 (256-32y + y 2) + 2y 2 \u003d 260
512-64y + 4y 2 -260 \u003d 0
4y 2 -64y + 252 \u003d 0
D \u003d 4096-16x252 \u003d 64
x 1 \u003d 9
x 2 \u003d 7
Now let's take into account that based on the fact that x + y \u003d 16 (see above) for x \u003d 9, then y \u003d 7 and vice versa, if x \u003d 7, then y \u003d 9
Answer: The sides of the rectangle are 7 and 9 centimeters
Problem 2. Find the sides of a rectangle from the perimeter
The perimeter of the rectangle is 26 cm, and the sum of the areas of the squares built on its two adjacent sides is 89 sq. see Find the sides of the rectangle.
Decision.
Let's denote the sides of the rectangle as x and y.
Then the perimeter of the rectangle is:
2 (x + y) \u003d 26
The sum of the areas of squares built on each of its sides (squares, respectively, two and these are squares of width and height, since the sides are adjacent) will be equal
x 2 + y 2 \u003d 89
We solve the resulting system of equations. From the first equation we deduce that
x + y \u003d 13
y \u003d 13-y
Now we substitute into the second equation, replacing x with its equivalent.
(13-y) 2 + y 2 \u003d 89
169-26y + y 2 + y 2 -89 \u003d 0
2y 2 -26y + 80 \u003d 0
We solve the resulting quadratic equation.
D \u003d 676-640 \u003d 36
x 1 \u003d 5
x 2 \u003d 8
Now let's take into account that based on the fact that x + y \u003d 13 (see above) for x \u003d 5, then y \u003d 8 and vice versa, if x \u003d 8, then y \u003d 5
Answer: 5 and 8 cm
Problem 3. Find the area of \u200b\u200ba rectangle from the proportion of its sides
Find the area of \u200b\u200ba rectangle if its perimeter is 26 cm and the sides are proportional as 2 to 3.
Decision.
Let's denote the sides of the rectangle through the proportionality coefficient x.
Whence the length of one side will be 2x, the other - 3x.
Then:
2 (2x + 3x) \u003d 26
2x + 3x \u003d 13
5x \u003d 13
x \u003d 13/5
Now, based on the received data, we determine the area of \u200b\u200bthe rectangle:
2x * 3x \u003d 2 * 13/5 * 3 * 13/5 \u003d 40.56 cm 2
Problem 4... Change the length of the sides while maintaining the area of \u200b\u200bthe rectangle
The length of the rectangle is increased by 25%. By what percentage should the width be reduced so that its area does not change?Decision.
The area of \u200b\u200bthe rectangle is
S \u003d ab
In our case, one of the factors increased by 25%, which means a 2 \u003d 1.25a. So the new area of \u200b\u200bthe rectangle should be
S 2 \u003d 1.25ab
Thus, in order to return the area of \u200b\u200bthe rectangle to its initial value, then
S 2 \u003d S / 1.25
S 2 \u003d 1.25ab / 1.25
Since the new size a cannot be changed,
S 2 \u003d (1.25a) b / 1.25
1 / 1,25 = 0,8
Thus, the value of the second side must be reduced by (1 - 0.8) * 100% \u003d 20%
Answer: the width needs to be reduced by 20%.
Determine the shape of the measured object
Perimeter is the length of a closed contour of a geometric shape, and there are various formulas for calculating the perimeter of shapes of different shapes. Remember that if a shape does not have a closed path, then the perimeter of that shape cannot be calculated.
Start by finding the perimeter of a rectangle or square (especially if this is your first time doing this). Such figures have the correct shape, which makes it easier to find their perimeter.
Add the values \u200b\u200bof all sides to calculate the perimeter.
That is, in the case of a rectangle, write: length + length + width + width.
Apply different formulas to different shapes
To calculate the perimeter of a different shape, you need a formula. In real life, to find the perimeter of an object of any shape, simply measure the sides. You can also use the following formulas to calculate the perimeter of standard geometric shapes:
Square: perimeter \u003d 4 * side.
Triangle: perimeter \u003d side 1 + side 2 + side 3.
Irregular polygon: The perimeter is the sum of all sides of the polygon.
A circle: circumference \u003d 2 x π x radius \u003d π x diameter.
π is pi (a constant of approximately 3.14). If your calculator has a π key, use it to perform more accurate calculations.
The radius is the length of the line segment connecting the center of the circle and any point on that circle. The diameter is the length of the line segment passing through the center of the circle and connecting any two points on that circle.
Calculating area
The essence of the square of a geometric figure
Calculating the area bounded by a closed loop is like dividing the interior of a shape into 1-unit x 1-unit squares. Keep in mind that the area of \u200b\u200ba shape can be larger or smaller than the perimeter of that shape.
Apply different formulas to different shapes. To calculate the area of \u200b\u200ba figure of another shape, you will need a corresponding formula. You can use the following formulas to calculate the area of \u200b\u200bstandard geometric shapes:
Parallelogram: area \u003d base x height
Square: area \u003d side 1 x side 2
Triangle: area \u003d ½ x base x height
In some textbooks, this formula looks like this: S \u003d ½ah.
The radius is the length of the line segment connecting the center of the circle and any point on that circle.
The square of the radius is the radius value multiplied by itself.
Calculating the area of \u200b\u200ba rectangle around the perimeter
Calculating the area of \u200b\u200ba rectangle with a known perimeter and aspect ratio.
I confess that when I first saw a request to create an Area calculator that sounded like "Calculate the area from the perimeter", I was somewhat surprised, because it looked somewhat surreal.
However, then, after searching the Internet, I realized that the request is simply not complete, and most often it sounds like this: “Calculate the area of \u200b\u200ba rectangle if its perimeter is X and you know that,. " - and different things can be known that lead us to a decision. For example, the length of one of the sides, or the aspect ratio. The calculator below calculates the area of \u200b\u200ba rectangle depending on what else is known besides the perimeter. Dedicated to schoolchildren.