How to Use an Area Calculator for Different Geometric Shapes
The amount of space in a two-dimensional place, which is acquired by a shape is called the area of that particular shape. The area measurement unit is dimension square. Suppose we are measuring something in meters and if we calculate the area, then area measurement units will be m2.
There are many useful formulas to calculate the space acquired by easy shapes and simple shapes. In the sections below you will find not only the well-known formulas for triangles, rectangle, and circles but also other shapes, like parallelogram, kites or annulus.
There are many area calculator apps available on the internet. Some of the area calculation tools are available for free online. Apart from this, there are many area measurement calculators also available on the internet.
Area Measurement
As we discussed, the area is the amount of space acquired by shape, so it depends on the shape and size. We'll discuss different types of shapes and formulas for their formulas.
1. Area of Square
Square is a quadrilateral in which all sides are equal length and all angles are equal to 90°. Let the length of sides of the square is a unit then it’s the area will be a x a = a2.
2. Area of Rectangle
A rectangle is a quadrilateral in which opposite sides are of equal length and all the angles are equal to 90°. Let a be it’s length and b be its breadth then we can calculate its area by the formula. a x b = ab.
3. Area of Triangle
There are several formulas for the area of the triangle. We use them depending on the given information in the question.
When Base and Height are Given
When base and height are given and we need to find the area of a triangle then use the formula ½ x b x h. where b is the base of the triangle and h is given height.
When Two Sides and the Angle Between Them is Given
When two sides and angles between them are given and we need to find the area of a triangle then use the formula ½ x a x b x sin ℽ. where a and b are lengths of the given sides and ℽ is the angle between them.
When all Three Sides are Given
When all three sides are given of a triangle and we need to find the area of it then we can use the formula \[\sqrt{s(s-a)(s-b)(s-c)}\] where s is \[\frac{a+b+c}{2}\] . Here, a, b and c are the given sides of the triangle. This formula is also known as Heron's formula.
When Two Angles and a Side is Given
When two angles and a side is given and we need to find the area of a triangle then use the formula \[\frac{a^{2}\times sin\beta \times sin\gamma }{2sin(\beta +\gamma )}\] . where a is the length of given the side and β , 𝛄 are given two angles.
Area of a Right-Angled Triangle
There is a special type of triangle whose area can be formulated. A right-angled triangle is a triangle whose one angle is right-angled. If the base and height of the triangle are given to us as a and be then, the area will be ½ x base x height.
4. Area of Circle
The area of the circle can be calculated by the formula πr2 , where r is the radius of the circle. Let us suppose we have given diameter in the question then we’ll use the formula π(d/2)2 because we know that d = r/2.
5. Sector Area Formula
Area of sector formula can easily be calculated by the formula \[\frac{\alpha}{2\pi }=\frac{SectorArea}{CircleArea}\] Here, 𝞪 is the angle of the arc. On further solving we get,
Sector area = 𝞪/2π x πr2 because we know the area of a circle is πr2.
Finally, we’ll get the area as \[\frac{\alpha \times r^{2}}{2}\].
6. Ellipse Area Formula
Recall the area formula of the circle. It is nothing but for πr2. Where r is the radius, the distance from the centre to each point of the circumference. In the case of an ellipse, this distance is different (as shown in the picture). Hence instead of r, we need to counter these parameters. So, the formula of the area of the ellipse we get as π x a x b. Where a is semi-minor axes and b is semi-major axes.
7. Trapezoid Area Formula
The area of the trapezoid can be calculated by the formula ½ x (a + b) x h. Here, a and b are the length of parallel sides and h is the distance between them. There is another formula of area of trapezoid but it can be computed by simple manipulation of the above-mentioned formula. We know that arithmetic means of a and b is given as (a + b)/2 . Now let’s represent this by c then the area formula will become c x h.
8. Area of Parallelogram Formula
There are several formulas for the area of the parallelogram. We use them depending on the given information in the question.
When Base and Height are Given
When base and height are given and we need to find the area of a parallelogram then use the formula b x h.where b is the base of the parallelogram and h is given height.
When Sides and Angle Between Them are Given
When sides and angle between them are given and we need to find the area of the parallelogram then use the formula a x b x sin𝞪. Where a and b are given sides and 𝞪 is the angle between them.
When Diagonals and Angle Between Them are Given
When diagonals and angles between them are given and we need to find the area of parallelogram then use the formula e x f x sinθ where e and f are the length of diagonals and θ is the angle between them.
9. Area of Rhombus Formula
Similar to the parallelogram, we have several formulas to find the area of the rhombus. We use them depending on the given data.
When Side and Height are Given
When a side and height of the rhombus are given to us and we need to find the area of it then use the formula a x h. Where a is the length of the side and h is the given height of a rhombus.
When the Length of Diagonals are Given
When the length of diagonals are given to us and we need to find the area of the rhombus then use the formula ½ x e x f. Where e and f are the lengths of diagonals.
When a Side and an Angle is Given
When side and angle are given and we need to find the area of rhombus then us the formula a2 x sin𝞪. Where a is the length of sides and 𝞪 is the given angle.
10. Regular Polygon Area Formula
A regular polygon is a two-dimensional shape whose all sides and angles are equal. It can be further divided depending on the number of sides. For example, If the number of sides is 5 then it’s a pentagon. It's area can be calculated by the formula ¼ x n x a2 x cot(π/n) Where n is the number of sides and a is the length of a side.
Did You Know?
In higher mathematics to find areas of non-regular or simple shapes, we use Integration. The integration uses the core concept of the Riemann sum. In simple words, Riemann sum is a sum only and a new way to represent sum. What Integration does is, takes small areas and adds them up to get the total area on the plane. For finding such a small area, we use the area of the rectangle formula.
FAQs on Area Calculation Tool: Quick & Easy Methods
1. What is the basic concept behind calculating the area of a shape?
The basic concept of area is to measure the total two-dimensional space a shape occupies. For simple shapes like rectangles, this is calculated by multiplying its length by its width. The formula changes depending on the shape, but the principle of measuring the enclosed surface remains the same.
2. How does an online Area Calculation Tool simplify geometry homework?
An online Area Calculation Tool acts as an instant calculator for various geometric shapes. You simply select the shape (e.g., circle, square, triangle) and enter its dimensions (like radius, side length, or base and height). The tool automatically applies the correct mathematical formula to provide an accurate answer, helping you check your work or solve complex problems quickly.
3. What is the difference between area and perimeter?
Area and perimeter are two different measurements of a shape. Perimeter is the total distance around the boundary of a shape, measured in linear units (like cm, m). Think of it as the length of a fence needed to enclose a field. Area, on the other hand, is the total space inside that boundary, measured in square units (like cm², m²). It represents the size of the field itself.
4. How do you calculate the area of common shapes like squares, circles, and triangles?
Each shape has a specific formula based on its properties:
- Square: Area = Side × Side (s²)
- Rectangle: Area = Length × Width (l × w)
- Triangle: Area = ½ × Base × Height (½ × b × h)
- Circle: Area = π × Radius² (πr²), where π (pi) is approximately 3.14159.
5. Why is area always measured in square units (e.g., m², ft²)?
Area is measured in square units because it represents the number of unit squares that can fit inside a two-dimensional shape. For example, an area of 12 square meters (m²) means that 12 squares, each measuring 1 meter by 1 meter, would be needed to completely cover the surface. This two-dimensional measurement (length and width) is why the unit is squared.
6. How can you find a missing side of a rectangle if you already know its area?
If you know the area of a rectangle and the length of one side, you can find the missing side by rearranging the area formula. The formula is: Missing Side = Area ÷ Known Side. For instance, if a rectangle has an area of 50 cm² and a length of 10 cm, its width would be 50 ÷ 10 = 5 cm.
7. What is the best method to find the area of an irregular shape?
Calculating the area of an irregular shape, which doesn't have a standard formula, is often done using the decomposition method. This involves breaking down the complex shape into a combination of simpler, regular shapes like rectangles, squares, and triangles. You then calculate the area of each individual shape and add them together to find the total area of the irregular figure.
8. How is area calculation used in real-world examples?
Area calculation is crucial in many real-world applications. For example:
- In construction and interior design, it's used to determine the amount of flooring, paint, or tiles needed for a room.
- In agriculture, it helps farmers calculate the size of their fields to plan for seeds and fertilisers.
- In cartography, it's used to measure the size of geographical regions like lakes, parks, or countries on a map.
