Perimeters and Areas of Rectangles

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 as 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.

Related Topics

• Quadrilaterals and Rectangles
• Perimeters and Areas of Squares
• How to Find the Perimeter of Polygons?
• How to Find the Area and Circumference of Circles?

Rectangle’s area:

A rectangle’s area is the number of unit squares which is able o 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 \(= (l × w)\)

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 \(12 × 6=72\)

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 \(7 × 4=28\)

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 perimeter and area of rectangles

1)

2)

Answers

1. \(\color{blue}{42,104}\)
2. \(\color{blue}{60,200}\)