What is ‘Area’?
Area is defined as the measure of space enclosed within the boundary of a two dimensional shape such as a circle, a rectangle or even a hexagon. It is measured in square units. We can apply appropriate formulas to find the area of certain polygons like squares, rectangles and triangles. Let us now look at the formulas that are applied to find the area of a rectangle followed by finding the area of a square.
How do we find the Area of a Rectangle?
A rectangle is a polygon with four sides. The opposite sides of a rectangle are parallel and equal in length. A rectangle has four interior angles, each measuring 90 degrees.
The sides of a rectangle are represented by, length (l) and width (w).
We can determine the area of a rectangle using the formula:
Area of rectangle, A = length × width
or
A = l × w
Doors, notebooks, doormats and even a dollar bill are a few examples of objects in our daily lives that are rectangular in shape.
How do we find the Area of a Square?
We can find the area of a square by using the same formula applied to calculate the area of a rectangle. We know that a square has four sides of the same length, so,
Area of square, A = length × length
or
A = l × l
= \( l^2 \)
Solved Examples
Example 1: The length of a square piece of cardboard is 55 meters. Find the cost of painting this cardboard piece at the rate of $0.06 per square meter?
Solution:
A = \( l^2 \) [Formula for area of a square]
A = \( 55^2 \) [Substitute for l]
A = 3025 sq. meters [Square of 55]
As per the question, cost of painting 1 sq.m = $0.06
Thus, for 3025 sq.m,
Cost of painting = 0.06 × 3025
= $181.5
Hence, the cost of painting the piece of cardboard is $181.50.
Example 2: Find the area of a rectangle with length 20 centimeters and width 15 centimeters.
Solution:
A = l × w [Formula for area of a rectangle]
A = 20 × 15 [Substitute for l and w]
A = 300 sq. cm [Multiply]
So, the area of the rectangle is 300 square centimeters.
Example 3: The area of a rectangle with length 25 centimeters is 100 square centimeters. What is the width of the rectangle?
Solution:
A = l × w [Formula for area of a rectangle]
100 = 25 × w [Substitute for A and w]
\( \frac{100}{25} \) = w [Divide both sides by 25]
4 = w [Simplify]
or, w = 4 cm
So, the width of the rectangle is 4 centimeters.
Perimeter refers to the measure of the total length of the boundary of any two dimensional figure. It is expressed in the same unit as that of length, that is, meters, centimeters, inches and so on.
3D or 3 dimensional shapes are solids that have 3 dimensions, which are, length, width and height. Prisms, cubes, and spheres are a few examples of 3D solids.
Squares are a special type of rectangles and have sides of equal length and width.
Polygons are closed geometric shapes with 3 or more sides. The sides of polygons are straight lines. Triangles, rectangles, pentagons and hexagons are a few examples of polygons. Also, a triangle is the smallest polygon with three sides.