What is the formula to find the area of a rectangle?
Rectangle
A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel. At that place are many rectangular objects effectually usa. Each rectangular shape is characterized past 2 dimensions, its length, and width. The longer side of the rectangle is known as the length and the shorter side is known equally the width. In this affiliate, we volition acquire most the rectangle shape and its properties.
| 1. | What is a Rectangle? |
| 2. | Properties of a Rectangle |
| 3. | Diagonal of a Rectangle |
| iv. | Area of a Rectangle |
| 5. | Perimeter of a Rectangle |
| half dozen. | FAQs on Rectangle |
What is a Rectangle?
A rectangle is a airtight two-dimensional figure with four sides. The reverse sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°. Find the rectangle given below to see its shape, sides and angles.
Properties of a Rectangle
A rectangle is a closed figure which has four sides and the angle formed by next sides is 90°. A rectangle can have a wide range of properties. Some of the important properties of a rectangle are given below.
- A rectangle is a quadrilateral.
- The opposite sides of a rectangle are equal and parallel to each other.
- The interior angle of a rectangle at each vertex is 90°.
- The sum of all interior angles is 360°.
- The diagonals bisect each other.
- The length of the diagonals is equal.
- The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is, diagonal = √( a2 + b2).
- Since the sides of a rectangle are parallel, it is also called a parallelogram.
- All rectangles are parallelograms but all parallelograms are not rectangles.
Diagonal of a Rectangle
The diagonal of a rectangle is a line segment that joins whatsoever two of its not-adjacent vertices. In the following rectangle, AC and BD are the diagonals that are equal in length. A diagonal cuts a rectangle into 2 right-angled triangles, in which the diagonal forms the hypotenuse, and the two adjacent sides of the rectangle form the other 2 sides of the triangle.
Diagonal of Rectangle Formula
The formula for the diagonal of a rectangle is derived using the Pythagoras theorem. Following the effigy given above, let us consider a rectangle of length 'l' and width 'west'. Allow the length of each diagonal exist "d". Applying Pythagoras theorem to the triangle ABD, dii = ltwo + due west2. Taking square root on both sides, √(d2) = √( fiftytwo + w2). Thus, the diagonal of a rectangle formula is diagonal (d): √(50² + westward²) and thus the diagonals of a rectangle can be calculated when the length and width of the rectangle are known.
Diagonal of Rectangle (d) = √(l² + w²)
Area of a Rectangle
The expanse of a rectangle is the number of unit squares that can fit into a rectangle. In other words, the space occupied by a rectangle is the surface area of the rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting sail, etc. We tin utilise the formula of the area of a rectangle to find the infinite occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches. Let us draw unit of measurement squares inside the rectangle. Each unit square is a foursquare of length i inch. At present, count the number of unit squares in the below figure. How many squares tin you lot observe? There are 12 squares in all. Nosotros accept already learned that expanse is measured in foursquare units. Since the unit of this rectangle is given in inches, the area is measured and written in square inches. Thus, the Surface area of the rectangle = 12 square inches. Thus, the surface area of a rectangle can be calculated when its sides (length and width) are known.
Area of Rectangle Formula
The formula for the area of a rectangle whose length and width are 'l' and 'due west' respectively is the product of its length and width, that is:
Surface area of a Rectangle = (l × w)
Perimeter of a Rectangle
The perimeter of a rectangle is the length of the total purlieus of a rectangle. Information technology tin be taken equally the sum of the total measure of the length and width of the rectangle and it is expressed in linear units similar cm, inches, and so on. For example, if y'all need to decorate the edge of your rectangular notebook, you can easily calculate how much ribbon you lot would need past finding the perimeter or if you need to put a fence around your garden, the perimeter of the garden will requite you the exact length of wire yous would need. The formula used to calculate the perimeter of a rectangle is explained below.
Perimeter of Rectangle Formula
The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'due west' respectively is ii(50 + w).
Perimeter of a Rectangle Formula = 2 (Length + Width)
Types of Rectangles
A quadrilateral whose contrary sides are equal and side by side sides meets at 90° is called a rectangle. A rectangle has two equal diagonals. The length of the diagonals is calculated by using the length and width. There are two types of rectangles:
- Square
- Gilded Rectangle
Square
A square is a closed ii-dimensional shape with four equal sides and four equal angles. It is a type of rectangle in which all iv sides are equal. The interior angle at each vertex is 90º which satisfies the definition of the rectangle. Observe the foursquare given below which fulfills all the properties of being a rectangle.
Golden Rectangle
A golden rectangle is a rectangle whose 'length to the width' ratio is similar to the gold ratio, i: (1+⎷v)/2. Its sides are defined co-ordinate to the golden ratio, that is, 1: i.618. For case, if the width is about 1 foot long and so the length will exist 1.168 feet long.
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What is a Rectangle in Geometry?
A rectangle is a 2-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles. The shorter side of a rectangle is called its breadth (width) and the longer side is the length. One of the most common geometrical figures that we come across in our twenty-four hours-to-mean solar day life is a rectangle.
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- 3D Shapes
- Geometric Shapes
How to Find the Length of a Rectangle?
The length of a rectangle can be calculated if the perimeter and the width is known. For example, if the perimeter of a rectangle is 32 units and its width is 4 units, we can apply the perimeter formula to get the length. Perimeter of a rectangle = 2 (l + w). Let u.s. substitute the known values in the formula, 32 = two (length + 4). On solving this, we go length + 4 = 16, that is, length = 12 units. Similarly, if the area of the rectangle and the width is known, the length can be calculated by using the formula for the area of a rectangle and substituting the known values.
How to Observe the Width of a Rectangle?
The width of a rectangle can be calculated if the area and the length is known. For example, if the area of a rectangle is 48 units and its length is 12 units, we can apply the expanse formula to get the width. Area of a rectangle = l × west. Permit u.s. substitute the known values in the formula, 48 = 12 × width. On solving this, we get width = 48/12, that is, width = 4 units. Similarly, if the perimeter of the rectangle and the length is known, the width tin be calculated by using the formula for the perimeter of a rectangle and substituting the known values.
How to Find the Diagonal of a Rectangle?
The length of the diagonal of a rectangle can be calculated if the length and width is known. Since the diagonal of a rectangle forms a correct-angled triangle with its sides, the diagonal becomes the hypotenuse and its value can exist calculated using the Pythagoras theorem. For instance, if the length of a rectangle is given as iv units and the width is iii units, we can find the length of the diagonal using the formula, diagonal (d) = √(fifty² + w²). So, let us substitute the value of the length and width in it. Diagonal (d) = √(50² + westward²) = √(4² + 3²) = √(sixteen + nine) = √25 = 5 units.
Why is a Rectangle Not a Regular Polygon?
A regular polygon is a polygon in which all the sides are of equal length and all the angles are of equal measure. In a rectangle, only the opposite sides are of equal length, therefore, a rectangle is not a regular polygon.
☛ Also Bank check:
- Types of Polygon
- Area of Polygons
What is the Formula for the Area of a Rectangle?
The area of a rectangle is the space occupied by it. The area of a rectangle is the product of its length and width. The formula for calculating the surface area of a rectangle is: Surface area = Fifty × B; where (50) is the length and (B) is the width of the rectangle.
☛ Check out the list of formulas for easy calculations:
- Perimeter Formulas
- Volume Formulas
- Expanse Formulas
- Measurement Formulas
What are the Properties of a Rectangle?
The basic properties of a rectangle are as follows:
- The opposite sides are parallel and equal.
- All the angles are equal to 90°.
- The diagonals are equal and they bisect each other.
Is the Area of the Rectangle the Same as the Area of the Foursquare?
No, the area of the square is not necessarily the aforementioned as the area of the rectangle because every square is a rectangle merely all rectangles are non squares. The formula to calculate the area of a rectangle is, Surface area of rectangle = Length × Width, and area of a foursquare = (side)two.
How to Find the Perimeter of a Rectangle?
The perimeter of a rectangle is twice the sum of its length and width and it is expressed past the formula, Perimeter = ii (Length + Width). It is expressed in linear units like cm, inches, and then on.
What is a 3D Rectangle Called?
A 3D rectangle is chosen a rectangular prism. A rectangular prism is a prism whose bases are likewise rectangles. It has 6 faces in all, out of which there are 3 pairs of identical opposite faces, i.e., all the opposite faces are identical in a rectangular prism.
What does a Rectangle Look Like?
A rectangle looks like an elongated square in which two contrary sides are equal and parallel. A few common examples of rectangles can be seen in the screen of a laptop, a notebook, a mobile phone and then on.
Source: https://www.cuemath.com/geometry/rectangle/
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