Area Calculator

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Different geometrical shapes require specific formulas and measurements to calculate their areas. Knowing the areas of these shapes is essential across various sectors and disciplines. For instance, land area calculations are widely used in land management, agriculture, biology, ecology, and various applied sciences like physics, chemistry, and engineering. JAIN (Deemed-to-be University)’s area calculator is a convenient online tool that simplifies the process of calculating the areas of common shapes, such as squares, rectangles, triangles, and circles. This tool is especially useful for geometry homework or when online tools are permitted in class. Additionally, an area calculator is widely used by professionals in the fields of architecture, engineering, and the arts. They are also handy for DIY projects, gardening, and home improvements, helping users estimate material requirements for their projects.

What is Area in Mathematics?

In simple terms, the area refers to the size of a surface. It can also be described as a space covered by a flat shape. To understand better, try to imagine the area as the amount of paint required to cover the surface completely. There are several formulas available to calculate the area of basic shapes. We have discussed the areas of different shapes in the subsequent sections along with their formulas. If it’s your first time knowing about this concept, then today, you shall learn about the square area formula, rectangle area formula, circle area formula, and triangle area formula. Alternatively, you can also use the JAIN (Deemed-to-be University)’s area calculator to calculate the area of a specific shape.

Area of a square

The area of a square is calculated by multiplying the length of one of its sides by itself:

Square Area Formula = a × a = a², where a represents the side length.

Calculating the square area formula is very simple. You need to use only one measurement tool, such as a ruler or a measuring tape. However, in most practical situations, you may need to measure both sides first to confirm it is a square, which involves the same steps as measuring a rectangle.

Area of a rectangle

The formula for calculating the area of a rectangle is simple. You just need to multiply its two adjacent sides:

Rectangle Area Formula = a × b, where a is the width and b is the height.

The rectangle area formula is highly practical for everyday tasks, such as estimating materials for construction (tiles, decking, or siding), planning home décor (paint or wallpaper), or identifying how many servings a cake can provide. It’s one of the easiest shapes to compute.

Area of a circle

The formula to calculate the area of a circle is one of the most widely used in mathematical equations.

Circle Area Formula = πr², where r represents the radius of the circle.

To apply the circle area formula, you only need to know the radius of the circle. However, in many real-life scenarios, it is often more convenient to measure the diameter instead. For this reason, an area calculator usually accepts the diameter as input. In case you only know the radius, then you can easily calculate the diameter by multiplying the radius by two.

Area of a triangle

There are several formulas for calculating the area of a triangle, depending on which laws or theorems have been used. We have provided an overview of the different types of triangle area formulas that can used under different circumstances:

Scenario	Triangle Area Formula	Description
Base and Height	Triangle Area = (b × h) / 2	Base (b) and height (h) are used to calculate the area.
Two Sides and the Angle Between Them (SAS)	Triangle Area = 0.5 × a × b × sin(γ)	Requires two sides (a, b) and the angle (γ) between them.
Three Sides (SSS)	Triangle Area = 0.25 × √((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c))	Known as Heron’s formula, it uses all three sides (a, b, c) to calculate the area.
Two Angles and the Side Between Them (ASA)	Triangle Area = (a² × sin(β) × sin(γ)) / (2 × sin(β + γ))	Requires one side (a) and two angles (β, γ).
Right Triangle (Base and Height)	Right Triangle Area = (a × b) / 2	Simplified formula for right triangles where a and b are the base and height forming the right angle.

Final Thoughts

Understanding the formulas and methods for calculating the areas of different shapes is essential across diverse fields. By mastering these formulas, you can efficiently tackle real-world challenges, such as estimating materials for construction, planning home improvements, or solving geometry problems. If you are seeking a quicker and more accessible solution, JAIN (Deemed-to-be University)’s area calculator offers a user-friendly tool to compute the areas of various shapes with ease and precision.

FAQs

How to calculate an area?

There are different formulas used to calculate the area of different shapes. Let us have a look at the area of some of the common shapes:

Square = S2 or Side x Side
Rectangle = Width x Height
Circle = πr² (r implies the radius of the circle)
Triangle = – ½ x base x height

How to calculate the area of an uneven rectangle?

To calculate the area of an uneven rectangle, you need to first identify and measure all the unknown sides. Next, you need to divide the irregular shape into smaller, regular shapes such as squares and rectangles. After this step, you have to calculate the area of each square or rectangle using their respective formulas. Finally, sum up all the individual areas to determine the total area of the irregular shape.

How to calculate land area?

There are different measurement units used to calculate the land area, such as square metres, square feet, acres, hectares, etc. Calculating a land area can also be a time-consuming and tedious process if done manually. Therefore, using an online land area converter can be easy to use and will also help save time and reduce errors in calculation.

How to calculate area in mm?

To calculate the area in square millimetres (mm²), you can use the following conversion:

Area in square millimeters (mm²) = Area × 100,000,000

This is because 1 area is equal to 100 square meters (m²), and 1 square meter is equal to 1,000,000 square millimetres (mm²). Therefore, the area multiplied by 100,000,000 will give you the area in square millimetres (mm).

How to calculate the area of a square?

You can calculate the area of a square by using the formula – S2 or Side x Side.

How to calculate the area of a rectangle?

You can calculate the area of a rectangle by using the formula – Width x Height.

How to calculate the area of a circle?

You can calculate the area by using the formula – π x radius².

How to calculate the area of a triangle?

You can calculate the area by using the formula – ½ x base x height.

What is the area of a 4 cm square?

By using the formula Side2, the area of a 4 cm square equals 16 cm.

What is a formula for the area of a rectangle?

The formula for the area of a rectangle is Width x Height.

How to calculate the area of land with 4 unequal sides?

To calculate the area of land with four unequal sides, you can break the irregular shape into smaller, more manageable shapes, such as triangles or rectangles. Here's how you can do it:

Start by dividing the land into smaller triangles or rectangles. This will make it easier to calculate the area of each part.
Use the appropriate formula to calculate the area of each individual triangle or rectangle.

Triangle Area = ½ x base x height
Rectangle Area = width x height

Once you have calculated the area of each smaller shape (triangle or rectangle), simply add them together to get the total area of the entire land.

What is the perimeter of a rectangle?

The perimeter of a rectangle is 2 (length + width).

What is the area formula?

The area formula depends on the shape you are calculating the area for. Here are the formulas for the areas of common shapes:

Square = Side2
Rectangle = Width X Height
Circle = π x radius2
Triangle = ½ x Base x Height

What is the area and perimeter of a circle?

The area of a circle is π x radius², whereas the formula for its perimeter is 2 x π x radius.

What is πr2?

π r2 is the formula for the area of a circle, where r stands for the radius (1/2 x diameter).

What is 2πr?

2 π r is the formula for the perimeter of a circle, where r stands for the radius (1/2 x diameter).

How to get an area of a triangle with 2 sides?

To calculate the area of a triangle with two sides, you need to know the included angle between those sides. Based on the Side-Angle-Side (SAS) formula, the area can be calculated as follows:

If you know sides 'b' and 'c' along with the included angle A, use the formula:

Area = ½ x b x c x Sin (A)

If you know sides 'b' and 'a' along with the included angle B, the area is:

Area = ½ x b x c x Sin (B)

If you know sides 'a' and 'c' along with the included angle C, the area is:

Area = ½ x b x c x Sin (C)

What is the formula for the area of a triangle?

The basic formula for the area of a triangle is ½ x base x height.