The rectangle area can be calculated with the help of its diagonals as given below.īy applying the Pythagoras Theorem, we getĪs we know that the rectangle area is the multiplication of length and widthīy putting the 2nd equation of width, we getĪrea of Rectangle = Length × √(Diagonal)² – (Length)²īy putting the 1st equation of length, we getĪrea of Rectangle = √ (Diagonal)² – (Width)² × width Rectangle Properties
Hence proved that the Area of a Rectangle is = Length x Breadth (Width) Area of Rectangle Using Diagonals Since Area of Rectangle ABCD = Area of ∆ABC + Area of ∆ADCįrom the 1st and 2nd expressions, we have Now considering diagonal AC bisects the rectangle into two right-angled triangles like ∆ABC and ∆ADC.Īs we know that ∆ABC and ∆ADC are identical right-angled triangles.Īrea of ∆ABC = ½ x Base of ∆ABC x Height of ∆ABC = ½ x AB x BC = ½ x B x L ……….1Īrea of ∆ADC = ½ x Base of ∆ADC x Height of ∆ADC = ½ x CD x AD = ½ x B x L ……….2 Hence, the rectangle area is equivalent to the addition of the area of two right-angled triangles. The diagonals of a rectangular shape bisect the shape into 2 similar right-angled triangles. The area of any figure like a rectangle or else is always represented in square units.Ī = L × B (in square units) Area of Rectangle Formula’s Proof Then the formula to find out the rectangle area will be the product of length and breadth. Let the length of a rectangle is ‘L’ and its breadth or width be ‘B’ and the Area of a Rectangle be indicated by ‘A’. The area of a rectangle can be enumerated by the product of its breadth and its length. The rectangle area is the region covered inside the outer boundary of the rectangle made by its four sides. The rectangular region covered by the perimeter of the rectangle is the area of a rectangle. The formula for the area of a rectangle is equivalent to the multiplication of the length and breadth of the rectangle. The surface area extended by a rectangle depends on its four sides.
All four internal angles of a rectangle are right angles (90 °). In the study of geometry, the area of a rectangle is defined as the region enveloped by the rectangle in a 2-dimensional plane. In this article, we provide you with the properties of a rectangle, the area of a rectangle, its formulas, and some relevant question answers for a better understanding of the concepts of the rectangle. In our day-to-day life, we see several rectangular-designed stuff like tables, books, boxes, mobile phones, walls, television, beds, almirah, etc. A rectangle is defined as a quadrilateral figure having four sides and the opposite sides are similar in length and parallel to one another. In a rectangle, the opposite sides and angles are the same in value. Yeah, it's more natural this way, thanks :) Also I have corrected an error in the computation of $x$ and $y$ in my previous answer.Area of Rectangle: A rectangle is a 2-D plane figure that has 4 sides and 4 internal angles. I have incorporated comment into the answer. The area of the smaller rectangle is $xy = 12$, so the area of the inscribed rectangle is $4xy = 4 \cdot 12 = 48$. Since $(x, y)$ is in the first quadrant, we have $x = 3\sqrt$. Plugging it into the equation of the ellipse, we have The sides of the smaller rectangle are $x$ and $y$ respectively so we have $x \colon y = 3 \colon 2$. Hence, the area of the inscribed rectangle is $2^2 = 4$ times that of the smaller rectangle. If $P = (x, y)$ is the vertex of the inscribed rectangle at the first quadrant, then the smaller rectangle spanned by the origin and point $(x, y)$ is similar to the inscribed rectangle.Įach side of the inscribed rectangle is $2$ times that of the smaller rectangle. In this case, the inscribed rectangle is also centered at the origin. We're lucky that the ellipse is centered at the origin.
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