What is the Area of Different Shapes?
The size of a two-dimensional surface is known as area. It is described as the measure of two-dimensional space a shape takes up. Formulas to calculate the area are used extensively in research, agriculture, building, and other fields. One way to calculate the area of a shape is by laying it on a grid and counting the number of squares completely covered by the shape.
For instance, with ‘a’ as the side length, we can obtain the area of a square with the formula, Area = a\( ^2 \).
Various area formulas are used to determine the area of various geometrical shapes. Squares, rectangles, circles, triangles or trapezoids are a few of the significant geometric figures.
Formulas to Calculate Areas of Different Shapes
Area Formula for a Rectangle
The length and width of a rectangle are multiplied to determine its area. The formula for calculating a rectangle’s area is:
\( \text{Area of Rectangle} = \text{Length} \times \text{width} = l \times w \)
Area Formula for Square
Finding the square of the length of each side of a square allows us to determine its area. The formula for calculating area of square is:
\( \text{Area of Square} = \text{Side} \times \text{Side} = \text{Side}^2 \)
Area Formula for a Triangle
Calculating a triangle’s area requires us to determine the product of the lengths of the base and height of a triangle, and this product is then divided by two. The formula for the area of a triangle is:
\( \text{Area of a Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times b \times h \)
Area Formula for a Circle
Finding the product of pi and the square of the radius of a circle will result in the area of a circle. The formula for the area of a circle is:
\( \text{Area of a Circle} = \pi r^2\)
Area Formula for Trapezoid
A trapezoid’s area is equal to half of the sum of the lengths of its parallel sides multiplied by its height. The formula for a trapezoid’s area is as follows:
\( \text{Area of a Trapezoid} = \frac{1}{2} \times \text{Sum of Parallel Sides (a + b)} \times \text{Height(h)} = \frac{1}{2} \times (a + b) \times h \)
Rapid Recall
The table here serves as a quick reference for the formulas to calculate the area of different shapes.
Solved Examples
Example 1. What is the size of a square plot whose sides are \( 41 \) meters long?
Solution:
As suggested in the question,
Side \( = 41 \) meters
Area of the square \( = \) side\( ^2 \) [Formula for the area of a square]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= (41 \times 41) \) m\( ^2 \) [Substitute the value]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1681 \) m\( ^2 \)
Hence, the area of the square plot is \( 1681 \) square meters.
Example 2. What is the surface area of a pizza with a \( 25 \) centimeter diameter? (Use \( \pi = 3.14 \))
Solution:
As suggested in the question,
Diameter \( = 25 \) cms
Radius \( = \frac{\text{Diameter}}{2} \)
\( ~~~~~~~~~~~= \frac{25}{2} \)
\( ~~~~~~~~~~~= 12.5 \) cms
Area of the circle \( = \pi r^2 \) [Formula for the area of a circle]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~= \pi (12.5)^2 \) cm\( ^2 \) [Substitute the value]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 3.14 \times 156.25 \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~=490.625 \) cm\( ^2 \) [Multiply]
Hence, the area of the circular pizza is \( 491 \) square centimeters.
Example 3. What is the area of a rectangle with dimensions of \( 23 \) meters in length and \( 19 \) meters in width?
Solution:
As suggested in the question,
Length of the rectangle \( = 23 \) meters
Width of the rectangle \( = 19 \) meters
Area of the rectangle \( = \) length \( \times \) width [Formula for the area of a rectangle]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= (23 \times 19) \) [Substitute the values]
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=437 \) m\( ^2 \) [Multiply]
Hence, the area of the rectangle is \( 437 \) square meters.
The formula for the area of a square is the product of the length of one of its sides multiplied by itself.
The area of the rectangle is the product of the length and the width.
The area formula can be used to determine the entire area a shape covers in a 2-D plane. Depending on the kind of shape and the inputs provided, there are multiple formulas to find the area of various shapes.