Area of RectangleA rectangle is a polygon that has four sides. The property of a rectangle is that the length of the opposite sides must be equal. We can find the area of a rectangle by using the formula that includes height and width. In this section, we will learn how to find the area of a rectangle and will try to understand through examples given in the last of this section. DefinitionThe area of a rectangle is the reign covered by a rectangle in a 2D plane. In other words, the width multiplied by its height. The unit of area is square units. Area of Rectangle FormulaWe can calculate the area of a rectangle if we know its height and length. Area of rectangle (A) = w * h Where w represents the width, and h represents the height. Sometimes we have given diagonal and width of a rectangle. Then we apply the following formula to find the area of a rectangle. Area of rectangle (A) = width√diagonal^{2}width^{2} Properties of Rectangle
In the above figure, the red color sides are of the same length and parallel to each other. Similarly, the green color sides are of the same length and parallel to each other. The right angle inside the rectangle denotes the angle, each of 90°. ExampleWhen width and height are given Example 1: Find the area of a rectangle whose height is 5 m and width is 9 m. Solution: Given, h=5 m and w=9 m We know that, area of rectangle (A) = w * h putting the values in the above formula, we get A = 9 * 5 A = 45 m^{2} The area of the rectangle is 45 m^{2}. When diagonal and width is given Example 2: Find the area of a rectangular board whose diagonal length is 20 cm and width is 13 cm. Solution: Given, length of diagonal (d) = 20 and width is 13 cm We know that, Area of rectangle (A) = width√diagonal^{2}width^{2} A = 13 √20^{2}13^{2}2 A = 13 √(400169) A = 13 √231 A = 13 * 15.19 A = 197.58 cm^{2} The area of rectangle is 197.58 cm^{2}. Using Pythagoras theorem Example 3: If the diagonal of a rectangle ABCD is 100 cm and its length x is twice its width y. Find the area of the rectangle. Solution: Given, diagonal (d) = 100 cm and width (x)= 2y According to the Pythagoras theorem: Hypotenuse=√base^{2}+perpendicular^{2} Putting the values in the above equation, we get: 100^{2}= y^{2} + (2y)^{2} 100^{2}= y^{2} + 4y^{2} 100^{2}= 5y^{2} on solving the above equation, y=20√5 putting the value of y in width, we get: we know that, Area of triangle (A) = width * height Since, A = 40√5 cm^{2} The area of rectangle is 40√5 cm^{2}.
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