In Euclidean Geometry, any shape that is a two-dimensional closed polygon with four sides is known as a quadrilateral. If the four sides meet at right angles where the opposite sides are parallel and equal is known as a rectangle. There are several concepts associated with it, such as area of rectangle, properties, perimeter, etc., that students must learn. This article will cover the basics of these topics. A rectangle is also equiangular as all the angles measure 90 degrees. Additionally, a rectangle is a special case of a parallelogram.
Area of a Rectangle
The area of a rectangle can be defined as the space enclosed within the four boundaries of the figure. To derive the area of a rectangle, we use the concept of a triangle. If we draw a diagonal from one vertice to the opposite one, then the diagonal so formed divides the rectangle into two equal right triangles. Thus, if we find the area of one triangle by doubling it, we can get the area of a rectangle. Suppose we have a rectangle with side lengths given by m and n.
- The area of a right triangle is given by ½ * base * height. The two sides of a rectangle form the length of the base and height. Hence, ½ * m* n gives the area of 1 right triangle.
- Now we have to multiply this result by a value of 2 as the diagonal forms two triangles, and we have the value of only one.
- Thus, the Area of a rectangle = 2 * ½ * m * n = m * n.
- The area is measures in square units.
Perimeter of a Rectangle
Perimeter is defined as the sum of the lengths of all the sides of that figure. Hence, suppose we have a rectangle with side lengths equal to m and n, then the formula for perimeter is given as
Perimeter of a rectangle = m + n + m + n (As the opposite sides are equal) = 2m + 2n = 2 (m + n).
Properties of Rectangles
- The opposite sides of a rectangle are equal in measure and parallel to each other.
- All the interior angles are right angles, and they sum up to 360 degrees.
- The length of the two diagonals are equal
- Both the diagonals are bisectors of each other and lie within the figure.
- A rectangle is a quadrilateral and a parallelogram
- A square is a special case of a rectangle that has all sides equal, and diagonals bisect each other at right angles.
- The diagonals of a rectangle bisect each other at different angles – obtuse and acute.
- Five degrees of freedom can be used to define a rectangle in a plane.
- If we rotate a rectangle along the line joining the midpoint of the longer parallel sides, then we get a cylinder whose height is given by the width of a rectangle, and diameter is the length of that rectangle.
- Similarly, if we rotate a rectangle along the line joining the midpoint of the shorter sides, we once again obtain a cylinder that has a height equal to the length of the rectangle, and diameter equals the width.
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