# Calculating the area of a shape: 7 Ways to Find the Area of a Shape

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## Area | Math ∞ Blog

In math, geometry is the science of finding the measurements of shapes. There are several different measurements that can be calculated depending on the type of shape. These measurements are called dimensions. Width, depth, or height are examples of dimensions.

Shapes can be broken into planes, geometric figures, or even just a point. Planes only have two dimensions such as length and width. Three-dimensional shapes have length, width and height. A point would only have one dimension. While a point doesn’t take up enough space to calculate for, planes and geometric figures do. This means planes and geometric figures have an area that can be calculated.

For each shape, there is a different formula to find its area. Three-dimensional shapes have surface area since space inside them will need to be calculated differently. The area inside a three-dimensional shape is called volume. Since calculating three dimensions is much more complex, it’s easier to focus on learning how to find the areas of two-dimensional shapes first.

Dimensions of Plane Shapes

A two-dimensional shape does not have volume, so calculating the area inside that shape is much easier. Depending on type of shape those dimensions have different names to make them distinct and avoid confusion when making measurements. For example, a square has length and width while a triangle would have base length and perpendicular height.

To make things clearer when measuring less conventional shapes, the angles along the perimeter of the shape also have names. A right triangle has a right angle, a curved triangle has both a rising and falling angle.

Measuring Areas

The measurements along the outside of the shape are taken in regular units. However, the area is measured in square units to account for volume. Regular units only measure in a straight line, squared units’ measure over an area. Squaring a unit of measurement is simple, it just needs to be multiplied by itself.

Squares are considered the most basic shape, so they have the most basic formula, S2. The variable of S stands for the measurement of one side. So, the area of a square can be found by measuring one side and multiplying it by itself. If the side of a square is five centimeters, the area of the square is twenty-five square centimeters.

Even though a rectangle also has flat sides, the formula is different. Multiplying the length and width will give the area of a rectangle.

Measuring the area of curved shapes is a little different. For irregular shapes, such as a lawn, control points can be created. This is done by finding the widest points of the shape and measuring to the opposite side. The measurement in between is called a line segment. These lines can have specific names. For example, a line that only goes half way across is called the radius. This line segment can be used to find other measurements in the circle. The diameter is found by multiplying the radius by two.

When measuring the area of curved shapes Pi will most likely be used in the formula. To find the area of a circle the formula is 2x Pi x radius. With a radius of four centimeters, the formula would be 2x 3.14 x 4 with a solution of 25.12 square centimeters.

For each unique shape, the formula to find its area will need to be used. There are dozens of formulas for finding area and each can be useful in its own way.

By finding the correct formula solutions to real world problems can be found easily.

## How To Calculate Area Of Land Or Plots Which Are Irregular In Shape

If you are a surveyor or owner of land in which you want to calculate the area of land then, you are at the right place. There are always common problems found in the surveyor or students to find out the area of an irregular land.

If the land is in square rectangular, triangular then we can easily find the area of land using simple geometrical formula. we will discuss how can we calculate the area of all types of land one by one.

All plots or land are not in fix geometrical shapes like a triangle, rectangle, or square. So, we often have to face difficulties to calculate the area of these kinds of land which are not in fixed geometrical shape.

Let us describe and make clear sense among all probable types and shapes of land which generally we have to calculate.

#### 1) Triangular Plots or Land

These types of land are rarely found, but it does not mean that you will not have to face this problem. you can probably get these types of land at the corner of road edge ar turning point. so let us solve shortly these types of problem.

##### Q) Calculate the area of given triangular land having side 21 m, 13 m, and 20 m respectively.

Solution:-

Let, Given side of triangle be,

(AB) = (a) = 21 meter

(AC) = (b) = 21 meter

(AB) = (c) = 21 meter

We have,

So, at first calculate semi perimeters (s) = (a+b+c)/2 = (20+21+13)/2 = 27 m.

The Semiperimeter of the triangle is half of its perimeter i.e (sum of their sides).

Now using above formula we get,

Area of triangular land (A)

Hence, in this way we can calculate area of land which are in triangular shape. now let us calculate area of rectangular plots of land.

#### 2) Rectangular Plots or Land

These types of land are often found in all areas. The sides of land whose one side is equal to their opposite side and another side is equal to another side are known as rectangular land.

It’s all sides are perpendicular to each other i.e 90 degrees with each other. Let’s understand with the help of numerical and figure given below.

##### Q) Calculate the area of rectangular land having dimensions given in the figure below.

Solution, Here in the figure two sides are 14 meter and two side are 8 meter.

so, let Length (L) = 14 meter and Breadth (B) = 8 meter

We have,

So, Using above formula we get,

Area = L X B = (14 X 8) = 112 m2

Hence, in this way we can calculate area of land which are in rectangular shape. now let us calculate area of square plots or land.

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#### 3) Square Plots or Land

These types of land are also common in all areas. you will get the shape of land mostly and nearly in rectangular or in square shape. The sides of land whose all sides are equal to each other are known as square land.

It’s all sides are perpendicular to each other i.e 90 degrees with each other. Let’s understand with the help of numerical and figure given below.

##### Q) Calculate the area of square land having dimensions given in the figure below.

Solution, Here in the figure have all sides equal and 8 meters.

so, let Length (L) = 8 meter

We have,

Using above formula,

Area of Land (A) = (8 X 8 ) m2 = 64 m2

Hence, in this way, we can calculate the area of land which is in square in shape. now let us calculate the area of trapezium plots or land.

#### 4) Trapezium land

This type of land may be regular or may be irregular. I am describing here all types of land with examples. let us discuss all land with the help of figure and formula to calculate it.

A) Land having two side parallel to each other

These types are land is found at the side of the road edge and maybe made artificially for a different purpose. In this type of land two sides are parallel to each other but the other two sides are not. Let us understand with an example.

You can also calculate the area of above land by dividing land into two parts in rectangle and triangle which you can see in the figure by the green line.

After that you can again use formula of square and triangle to each other and get total area.

I hope you understood and you can calculate the area of these types of land. Let us see another type of irregular land which you generally found at the survey. but don’t worry I will do the numerical of this land also. so let us move forward.

B) Land having no any side parallel to each other

This type of land is mostly found in every place of state and country. This is irregular land. In these types of land, all sides are different from each other. and also they make different angles with each other.

Surveyors have to calculate these types of land so, often and they get more problems in such types of land to calculate actual area. let us understand with numerical and formula to calculate the area of land.

##### Q) Calculate the area of irregular land having dimension given in the figure below.

Solution,

To calculate these types of land is very easy. to find out the area of these types of land, first of all, burry four pegs or ranging rods at all corners of the land. after that take measurements of all sides of the land. and keep in mind you must take the measurement of any one of the diagonal plots.

Now, you can see in the figure, total land has been divided into two parts with blue line diagonals and they are triangles in shape.

That’s all, use the formula of triangular land separately and add both to get the total area. isn’t it easy?

Now, let us move on calculation,

In triangle ABD,

let, BD (a) = 5 meter, AD (b) = 3 meter, AB (c) = 4 meter

Again we have,

where, S = (a+b+c)/2 = (5 + 3 + 4)/2 = 6 meter.

So, Putting all values we get the Area of triangle ABD,

= A1 = 6 m2

In the same way, for triangle BDC,

let, DC (a) = 13 meter, BC (b) = 12 meter, BD (c) = 5 meter

where, we have (S) = (a+b+c)/2 = (13 + 12 + 5)/2 = 15 meter.

So, putting all value we get Area of triangle BDC,

= 30 m2

Hence total are of land become,

= Area of triangle ABD and triangle BDC

= A1 + A2

= (6 + 30) m2

= 36 m2

Enter Dimension of Land

Length of AB (feet):

Length of BC (feet):

Length of CD (feet):

Length of DA (feet):

Length of BD (feet):

#### Results

Total Area of Land in Feet Square :Total Area of Land in Meter Square :Total Perimeter of Land :

### For Nepal

Area in Dhur :Area in Kattha :Area in Bigha :Area in Ropani :Area in Anna :

Hence, in this way, we can calculate the area of land which is irregular in shape.

## Calculation of the area of ​​geometric shapes | International Institute of Care to Buildings

REFERENCES

The area of ​​a geometric figure is a part of the surface bounded by a closed contour of this figure. The size of the area is expressed by the number of square units contained in it.

### Triangle area formulas

#### 1st formula

S — triangle area

a, b — lengths of 2 sides of a triangle

С — angle between sides a and b

#### 2nd formula

S — area of ​​triangle

a — Triangle side length

h — length of the height lowered to side a

#### 3rd formula

S — area of ​​triangle

a, b, c — lengths of 3 sides of triangle

p — semiperimeter of triangle

#### 4th formula

S — area of ​​triangle

r — radius of inscribed circle

p — semiperimeter of triangle

9001 7 5th formula

S — area of ​​triangle

a, b, c — lengths of 3 sides of a triangle

R — radius of the circumscribed circle

See also: Online calculator for calculating the area of ​​a triangle .

### Formulas for the area of ​​a square:

1) The area of ​​a square is equal to the square of the length of its side (a).

2) The area of ​​square is half the square of the length of its diagonal (d).

S — area of ​​a square

a — length of a side of a square

d — length of the diagonal of a square

### Rectangle area formula:

1) The area of ​​the rectangle is equal to the product of the lengths of its two adjacent sides (a, b).

S — area of ​​the rectangle

a — length of the 1st side of the rectangle

b — length of the 2nd side of the rectangle

### Parallelogram area formula:

1) Parallelogram area is equal to the product of the length of its base and the length of its height (a, h).

S — area of ​​parallelogram

a — length of base

h — length of height

### Formula for the area of ​​a trapezoid:

1) The area of ​​a trapezoid is equal to the product of half the sum of its bases and the height (a, b, h).

S — trapezoid area

a — length of the 1st base

b — length of the 2nd base

h — length of the height of the trapezoid

See also: Online calculator for calculating the area of ​​a trapezoid .

### Formulas for the area of ​​a rhombus:

1) The area of ​​a rhombus is equal to the product of the length of its side and the height (a, h).

2) The area of ​​the rhombus is half the product of its diagonals.

S — area of ​​the rhombus

a — length of the base of the rhombus

h — length of the height of the rhombus

d 1 — length of the 1st diagonal

d 2 — length of the 2nd diagonal

See also: Online calculator for calculating the area of ​​a rhombus .

### Formula for the area of ​​a circle:

1) The area of ​​a circle is equal to the product of the square of the radius and pi (3.1415).

2) The area of ​​the circle is equal to half the product of the circumference of the circumference and the radius.

S — area of ​​a circle

π — pi (3.1415)

r — radius of a circle

See also: 900 89 Online calculator for calculating the area of ​​a circle .

### Ellipse area formula:

1) Ellipse area is equal to the product of the lengths of the major and minor semi-axes of the ellipse and the number pi (3.1415).

S — area of ​​the ellipse

π — pi (3.1415)

a — length of the semi-major axis

b 9000 4 — minor axis length

## Measure the area of ​​a compound figure

 Polinomial Chebyshev with a free member Create a vector (diophantine) from a matrix Egyptian fractions. Part two Egyptian (aliquot) fractions Determine the radius of a circle from a segment Circle and area intercepted by perpendiculars Division of a triangle into equal areas by parallel Determining the basic parameters of an integer Properties of inverse trigonometric functions Divide a ball into equal volumes by parallel planes The relationship between organisms with different types of metabolism Autotrophic and mixotrophic organisms Dissection of a circle by straight lines into equal areas Odd fraction period online. The first fifteen hundred expansions. Representing a fraction as the sum of its factors Solution of a system of two homogeneous Diophantine equations Calculation of the main parameters of a quadripole Chain of remainders from division in the ring of an integer Number system based on the Fibonacci series online Equation of the fifth degree. Private decision. Calculate the area of ​​a triangle by three sides online General solution of a linear Diophantine inhomogeneous equation Particular solution of a Diophantine equation with several unknowns Online expansion of a fractionally rational function Roots of the characteristic equation
 Side length of the «reference» square Weight of the «reference» square Weight paper copy of project Ratio of square length to real project length
 The area of ​​the project in the units specified in ‘The ratio of the length of the square to the length of the real project’

complex figure.

Such a problem may arise when calculating the area of ​​your palace or cottage or apartment that you have ever built or will build. The layout of the floors, for example, is very complex — with bends and semicircles, and the area must be calculated.

There are many options. You can draw our layout in a graphical editor and calculate the area. You can entrust it to specialists.

But we will use a very old, but simple and effective method.

So, we have a layout of such a strange building

1. Let’s print our layout on paper. The heavier the paper, the better the area calculation accuracy will be.

2. On the same paper, print a square. The length of the side of the square must match any known(!) straight side on our project. This is necessary in order to later convert square centimeters into square meters.

3. Cut out our floor plan from paper

4. Cut out a square from paper.

5. Measure the area of ​​the square. I hope the formula for such banality is not necessary? Let it be equal to 8 * 8 = 64 square centimeters

6. Crumple each of the resulting figures 🙂 So that it all fits on the scales.

7. Weigh two pieces of paper. Let the square weigh 10 grams, and our project 40 grams.

The last step remains.

Since our square and the project were cut from the same material with the same thickness, the relationship between the area and mass will be linear .

From this proportion, we know three quantities, and it is very easy to calculate the area of ​​the project.

As mentioned above, the weight of the square is 10 g, the weight of the project is 40 g, the area of ​​the square is 8*8=64 cm2

Then the area of ​​the paper project will be 256 square centimeters.

There is one nuance left, we calculated the area of ​​the project on paper, but how can we convert these square centimeters into meters? For this, it was not in vain that condition two was mentioned, under which we drew / printed a «reference» square.

we make one more proportion

The ratio of the project side in reality to the side of the project on paper is equal to the ratio of the square root of the area of ​​the real floor (project) to the square root of the project area on paper.

Again, we know three data. See the previous calculation0005

Then the area of ​​our project in reality will be exactly 20 * 20 = 400 square meters.

Now you can order materials for decoration and evaluate another front of work, so that you could live in this palace.

Pay attention to the material Find out the area of ​​the figure with a ruler or rangefinder

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