What is the definition of area?
The area of an object is the region bounded by its shape. The area of a shape is the space covered by that figure or two-dimensional geometric shape in a plane. The area of each shape is determined by its dimensions and properties. This means that different shapes will have different areas. The area of a square is not the same as that of a kite.
What is the definition of perimeter?
The total distance around a shape is defined as its perimeter. In simple terms, the perimeter of any shape is its length when expanded in a linear form. In a 2-d plane, a perimeter is the total distance that encircles a shape. Depending on their dimensions, the perimeters of different shapes can be of the same length.
For example, if a circle is made of steel wire of length L, the same wire can be used to make a square with equal sides of length.
What's the difference between perimeter and area?
The following is a list of the differences that exist between area and perimeter:
What is a rectangle?
A rectangle is a four-sided two-dimensional plane figure. A rectangle is a quadrilateral polygon where the opposite sides are parallel and have equal length. It’s one of the quadrilaterals in which all four angles are 90 degrees or right angles. A rectangle is a type of parallelogram where all angles are equal. A rectangle with four equal sides is known as a square.
Rectangle, the most common shape, is part of our daily life. Real-world examples of rectangles include tabletops, books, cell phones, and TVs.
Properties of rectangle
Rectangles have the following basic properties:
- A rectangle is a quadrilateral.
- The opposite sides are equal.
- The opposite angles are equal.
- The diagonals bisect each other and have the same length.
- The perimeter of a rectangle with side lengths l and w is 2( l + w ) units.
Formulas used to understand a rectangle
There are two main rectangle formulas that must be remembered. They are related to the area of a rectangle and the perimeter of a rectangle.
Area of a Rectangle: A = l x w, where l and w are the rectangle’s length and width, respectively.
Rectangle Perimeter: P = 2 x (l + w), where ‘l’ is the rectangle’s length and ‘w’ is its width.
Solved Examples
Example 1: Calculate the area and perimeter of a rectangle whose length and width are 14 cm and 10 cm, respectively.
Solution:
The properties of a rectangle can be used to calculate the area and perimeter of a rectangle. The rectangle’s length is 14 cm, and its width is 10 cm.
A rectangle’s area is equal to its length multiplied by its width.
Area of Rectangle = Length x Width
Area of Rectangle = 14 x 10 = 140 square centimeters.
Rectangle perimeter = 2 (length + width)
= 2 x (14 + 10) = 2 x (24) = 48 cm
Example 2: Calculate the area and perimeter of a rectangle whose length and width are 16 cm and 9 cm, respectively.
Solution:
The properties of a rectangle can be used to calculate the area and perimeter of a rectangle. The rectangle’s length is 16 cm, and its width is 9 cm.
A rectangle’s area is equal to its length multiplied by its width.
Area of Rectangle = Length x Width
Area of Rectangle = 16 x 9 = 144 \(cm^2\)
Rectangle perimeter = 2 (length + width)
= 2 x (16+9) = 2 x (25) = 50 cm
Example 3: Thomas built a rectangular castle in a video game that is four times longer than it is wide. What is the castle’s perimeter?
Solution:
Length of the castle = 4 × width of the castle
= 4 × 25 yd
= 50 yd
The properties of a rectangle can be used to calculate the perimeter of a rectangle. The rectangle’s length is 50 yd, and its width is 25 cm.
Now, the perimeter of the castle = 2 (length + width)
= 2 x (50 + 25) = 2 x (75) = 150 yd
Example 4: The rectangular dance floor’s length is 6 feet longer than its width. What is the dance floor’s size?
Solution:
Length of rectangular dance floor = width of rectangular dance floor + 6
= 24 + 6 = 30 ft
The properties of a rectangle can be used to calculate the area of a rectangle. The length of the rectangular dance floor is 30 ft, and its width is 24 ft.
A rectangle’s area is equal to its length multiplied by its width.
Area of Rectangular dance floor = Length x Width of rectangular dance floor
Area of Rectangular dance floor = 30 x 24 = 720 square feet.
Yes, a square is considered a rectangle because it has all of the properties of a rectangle, such as all four interior angles being 90 degrees, opposite sides being parallel and equal, and two diagonals being equal and bisecting each other.
A rectangle is a two-dimensional shape that has four sides, four angles, and four vertices. A rectangle’s opposite sides are equal and parallel to one another. A rectangle’s interior angles are equal and measure 90 degrees.
A rectangle’s basic properties are that its opposite sides are parallel and equal, and its interior angles are all 90 degrees. It also has equal diagonals that bisect each other.