Key Area Formulas for Squares, Triangles, Circles & More
Area of Shapes
The area of shapes is the space surrounded or enclosed with the boundary of perimeter of the given geometric shapes. It is a measurement that determines the magnitude of two-dimensional shape or planar lamina in the plane. The shape of the lamina includes two-dimensional figures that can be easily drawn on the plane such as square, rectangle, triangle, parallelogram, trapezium etc. Areas of shapes such as square, rectangle, triangle, parallelogram, trapezium, circle are the range covered by them in space. In this article you will study areas of geometric shapes, area formulas for different shapes, area of 2d shapes, area of 3d shapes etc.
Polygon Shapes
A polygon is a two-dimensional shape that is made up of straight lines. Some examples of polygon shapes are triangle, pentagon, hexagon, square, rectangle, etc. The name of these shapes itself determines the total number of sides included in the shape. For example- a triangle has 3 sides and a rectangle has 4 sides. Therefore, any shape that is made up of joining three lines is known as a triangle whereas the shapes that are made up of joining four lines are known as quadrilaterals. The area is the range inside the boundary/perimeter which is to be examined.
Area of 2d Shapes
In geometry, two-dimensional shapes are defined as the flat plane figure or shape that includes two measures such as length and breadth. There is no thickness in 2-d shapes. Area and perimeter are two different measures used for measuring flat shapes. The two-dimensional can be easily drawn on a plain paper. Some of the examples of 2-d shapes are rectangle, triangle, square, trapezoid etc.
Area of 2d Shapes Formula-
Generally, the area of shapes is defined as the quantity of paint color required to cover any of the surface with a single coat. Here are the methods to calculate area on the basis of sides included in the shape as described below:
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Here, you can see the Area Formulas for Different Shapes in Tabular Format.
Area of 3d Shapes
Three-dimensional shapes are the solid shapes that retain three-dimensions such as length, width and height.The two different measures used to determine three-dimensional shapes are volume and surface area. Generally, we get the three-dimensional shapes from the rotation of the two-dimensions shapes. The major difference between 2-d and 3-d shapes is that the 3-shapes have thickness whereas 2-d shapes do not have thickness. If you want to determine the surface area of any solid shapes, then it can be easily determined from the area of 2 d shapes.
Area of 3D Shapes Formula-
According to the international system of units (SI), the standard unit of area is meter square(m²). For example- a certain shape with an area of 4 square meters will have the similar areas as four such squares. The surface area of solid shapes is determined as a measure of a total area that the surface of the object covers.
Here, you can see the Area Formulas for all Shapes in Tabular Format.
Including the area of the planar shapes, an extra variable i.e the height of the variable is taken into consideration for calculating the surface area of shapes.
Examine a circle of radius r and draw boundless concentric circles.Now, from the center of a circle to its boundary , draw a line segment equivalent to the radius of a circle along with that segment. A triangle will be formed with a base equivalent to the circumference of a circle and height equivalent to the radius of the outer circle i.e. r. Thus the area can be calculated as ½ × base × height ie. ½ * 2πr².
Solved Examples-
1. Calculate the Area of the Circular Path whose Radius is 7cm.
Solution:
Radius of circular path = 7 cm (given)
As we know, the area of a circle is πr²
Accordingly,
Area = π × r × r
Area = 22/7 × 7 × 7
Area = 154 square metre
2. What will be the Breadth of a Rectangle, if its Area is 72cm and Length is 8 cm.
Solution:
As we now,
Area of a rectangle = length × breadth
Given that , area= 72cm and length = 8 cm
Let the breadth of a rectangle be a
As we now,
Area of a rectangle = length × breadth
Accordingly,
A = l × b
72 = 8 × a
72= 8a
a = 72/9
a= 8 cm
Hence, the breadth of a rectangle 8 cm.
3. Calculate the Area of a Cone whose Radius is 4cm and Height s 3cm’
Solution:
Radius of a cone = 4cm and height of a cone= 3 cm ( Gven)
As we now, the area of the cone is πr(r + l)
Slant height= l \[\sqrt{4²+3²}\] = \[\sqrt{25}\] = 5cm
Area of a cone = πr(r + l)
A = 22/7 × 4 (4 + 5)
A = 22/7 × 4(9)
A= 22/7 × 36
A = 113.14 cm²
Quiz Time
1. Two Equivalent Parallelograms have their Corresponding Sides in the Ratio of 1 : k.what will be the Ratio of their Areas.
1:3²
1:4²
1:k²
1:2k²
2. How will the Surface Area of a Sphere Change, if the Diameter of the Spheres is Doubled?
It will increase two times
It will increase three times
It will increase four times
It will increase eight times
3. What will be the Area of a Rectangle whose Altitude is Equal to 2\[\sqrt{3}\]cm
\[\sqrt{3}\]cm²
2\[\sqrt{3}\]cm²
3\[\sqrt{3}\]cm
4\[\sqrt{3}\]cm²
FAQs on Area of Geometric Shapes: Complete Guide
1. What is the basic definition of 'area' in the context of geometric shapes?
In geometry, the area is defined as the total two-dimensional space or region enclosed by the boundary of a geometric figure. It measures how much surface a shape covers and is always expressed in square units, such as square centimetres (cm²), square metres (m²), or square inches (in²).
2. What are the area formulas for the most common 2D geometric shapes?
The area formulas for common shapes are essential for solving various mathematical problems. Here are the key formulas:
- Square: Area = side × side = a²
- Rectangle: Area = length × width = l × w
- Triangle: Area = ½ × base × height = ½ × b × h
- Circle: Area = π × radius² = πr²
- Parallelogram: Area = base × height = b × h
- Trapezium: Area = ½ × (sum of parallel sides) × height = ½ × (a+b) × h
3. What is the primary difference between the area and the perimeter of a shape?
The primary difference lies in what they measure. Area measures the total surface covered by a shape, like the amount of grass in a field. In contrast, the perimeter is the total length of the boundary around the shape, like the length of the fence needed to enclose that field. Area is measured in square units (e.g., m²), while perimeter is a length measured in linear units (e.g., m).
4. Why is understanding the area of geometric shapes important in real-world applications?
Understanding area is crucial for many practical tasks. For example, you need to calculate the area of walls to determine the amount of paint required for a room. Similarly, you would calculate the floor's area to know how many tiles are needed. In fields like architecture, engineering, and even agriculture, calculating area is fundamental for planning, resource allocation, and design.
5. How do you find the area of a composite or complex shape?
To find the area of a composite shape, you break it down into simpler, standard shapes like rectangles, squares, triangles, and circles. The process involves these steps:
- Deconstruct the complex figure into its basic geometric components.
- Calculate the area of each individual component using its specific formula.
- Add or subtract the areas of these components as required to find the total area of the composite shape.
6. How does the concept of 'area' apply to 3D shapes like a cube or a sphere?
For 3D shapes, the concept of area evolves into Surface Area. Instead of measuring a flat 2D region, surface area is the sum of the areas of all the faces or surfaces that enclose the 3D object. For example, the surface area of a cube is the total area of its six square faces. This is different from volume, which measures the space inside the 3D shape.
7. Can two different shapes have the same area but different perimeters? Explain with an example.
Yes, it is possible for two shapes to have the same area but different perimeters. This illustrates that area and perimeter are independent properties. For instance:
- A rectangle with sides 8 cm and 2 cm has an area of 16 cm² (8 × 2) and a perimeter of 20 cm (2 × (8+2)).
- A square with sides 4 cm has the same area of 16 cm² (4 × 4) but a smaller perimeter of 16 cm (4 × 4).
