With the help of the perimeter, we can find the unknown side and then calculate the area using the same formula, Area of rectangle = Length × Width. The area of a rectangle can be calculated if the perimeter and one of its sides is given. So, let us apply the direct formula, Area of a Rectangle = Width ⎷Īfter substituting the values of diagonal = 10 units, and width = 6 units, we get, Area of a Rectangle = Width ⎷Īrea of the rectangle = 48 square units Area of Rectangle using Perimeter Solution: We know the diagonal and the width of the rectangle. Let us use an example to understand this.Įxample: Find the area of a rectangle in which the width is 6 units, and the diagonal is 10 units. We can use the same formula if we know the length and if the width is missing.Now, if we replace the above formula of length in the area of rectangle formula, then, the area of the rectangle formula can be expressed as follows, Area of rectangle = ⎷ × Width We know that the formula to calculate the area of a rectangle is, Area of rectangle = Length × Width.This formula can be used in place of the length. Here, the length is expressed in terms of the diagonal and width. Further, this can be expressed as, Length = ⎷. So this can also be written as, (Length) 2 = (Diagonal) 2 - (Width) 2. We know that (Diagonal) 2 = (Length) 2 + (Width) 2.For example, if the length of the rectangle is missing, and we know the diagonal and width, then we can express the length in terms of the width and the diagonal and then use it in the formula of the area of a rectangle.This method also applies the same logic but we use a direct formula to find the area of a rectangle. Now, we know that the length = 4 cm, width = 3 cm. In this case, the width can be calculated using the formula, width = ⎷Īfter substituting the given values, we get, width = ⎷ The width of the rectangle is missing and it can be calculated using the Pythagoras theorem because the diagonals of a rectangle form 2 right-angled triangles. Let us understand this using an example.Įxample: Find the area of a rectangle whose length is 4 cm and whose diagonal is 5 cm. We can find the value of the missing side using the Pythagoras theorem and then find the area. There can be two ways in which we can find the area of a rectangle using the diagonal. There are two diagonals in a rectangle and both are of equal length. The diagonal of a rectangle is the straight line inside the rectangle connecting its opposite vertices. The area of a rectangle can be calculated if the diagonal and one side is given. Similarly, if the length and width of any rectangle is given in cm, then the area will be expressed in square centimeters (cm 2). In this case, since the length and width of this rectangle is given in 'inches', the area is measured and written in square inches (in 2). In other words, 12 unit squares can fit in the given rectangle covering all its space and this is termed as the area of a rectangle. So, a rectangle whose sides are 4 inches and 3 inches has an area of 12 square inches or 12 in 2. Since 12 equal-sized squares can fit in this rectangle, they also show the space occupied by the whole rectangle. Observe the figure given below in which we can divide the figure into 12 small squares, each of which is a square, that is, 1 inch on each side, that is, 1 square inch. Now, let us understand the reason for which the area of a rectangle is expressed in square units using the following example.Įxample: The length of a rectangle is 4 inches and its width is 3 inches. We know that length is always measured and expressed in units like cm, inches, etc. The unit of the area of a rectangle is expressed in square units. Therefore, the area of the rectangle = 60 square units. Therefore, area of the rectangle = 15 × 4 = 60 Substitute 15 for 'l' and 4 for 'w' in this formula. The formula to find the area of a rectangle is A = l × w. Solution: Given, length = 15 units and width = 4 units. Let us take an example to understand the calculation of the area of a rectangle.Įxample: Find the area of the rectangle whose length is 15 units and width is 4 units. Step 3: Give the answer in square units.Step 2: Find the product of the length and width values.Step 1: Note the dimensions of length and width (breadth) from the given data.The area of a rectangle can be calculated using the steps given below: The area of a rectangle is the product of its length and width (breadth).
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