Perimeters and Areas of Rectangles
In this article, we will learn how to calculate the perimeter and area of a rectangle
Rectangles are closed \(2\)-dimensional figures having \(4\) sides. The opposing sides of rectangles are identical as well as parallel to one another as well and all the rectangle’s angles are equal \(90°\).
A few of the vital characteristics are rectangles shown here.
- Rectangles are quadrilaterals.
- The opposing sides’ rectangles are identical and parallel to one another.
- The inner angle of a rectangle at each of the vertexes equals \(90°\).
- The total of all inner angles equals \(360°\).
- Its diagonals bisect one another.
- The diagonals’ length is identical.
- The diagonals’ length can be achieved via the Pythagoras theorem. The diagonal’s length with sides a and b is, diagonal = \(\sqrt{(a^2+b^2})\).
- Because the rectangle’s sides are parallel, it’s additionally known as a parallelogram.
- Every rectangle is a parallelogram, however, not every parallelogram is a rectangle.
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Rectangle’s area:
A rectangle’s area is the number of unit squares which is able to fit into a rectangle. So, the space inhabited by the rectangle is the rectangle’s area.
The formula to get a rectangle’s area where the length and width are ‘\(l\)’ and ‘\(w\)’ individually is the outcome of its length and width, so:
Area of a Rectangle \(= (l × w)\)
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Rectangle’s perimeter
A rectangle’s perimeter is the length of the complete rectangle’s boundary. It may be taken as the calculation of the complete measurement of the rectangle’s length and width and it’s shown in linear units such as inches, centimeters, etc.
The formula to get the perimeter, ‘\(P\)’ of a rectangle where the width and length are ‘\(w\)’ and ‘\(l\)’ respectively is \(2(l + w)\).
Formula for the Perimeter of a Rectangle \(= 2 (Length + Width)\)
Perimeters and Areas of Rectangles – Example 1:
Find the area and perimeters of a rectangle with \(12\) cm length and \(6\) cm width
Solution:
The formula to get a rectangle’s area = Length × Width. So, the rectangle’s area is \(12 × 6=72\)
The formula for the perimeter of a rectangle = \(2\) (Length + Width). So, the perimeter of a rectangle \(= 2(12+6)=36\)
Perimeters and Areas of Rectangles – Example 2:
Find the area and perimeter of the rectangle
Solution:
The formula to get a rectangle’s area = Length × Width. So, the rectangle’s area is \(7 × 4=28\)
The formula for the perimeter of a rectangle = \(2\) (Length + Width). So, the perimeter of a rectangle \(= 2(7+4)=22\)
Exercises for Perimeters and Areas of Rectangles
Find the perimeter and area of rectangles
1)
2)
Answers
- \(\color{blue}{42,104}\)
- \(\color{blue}{60,200}\)
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