The area of a parallelogram whose diagonals are given by the vectors d 1 and d 2 is 1/2 |( d 1 × d 2)|.The area of a parallelogram whose adjacent sides are the vectors a and b is | a × b|.The area of the parallelogram can be calculated using different formulas even when either the sides or the diagonals are given in vector form.

d 1 and d 2 = Length of diagonals of the parallelogram, and.Suppose, this angle is given by x, then the area of the parallelogram is given by: There are two diagonals for a parallelogram, intersecting each other at certain angles. The area of any given parallelogram can also be calculated using the length of its diagonals. Note: If the angle between the sides of a parallelogram is 90 degrees, then the parallelogram becomes a rectangle. If the length of the two adjacent sides is 4 units and 6 units respectively, then find the area. a and b = length of adjacent sides, and,Įxample: The angle between any two sides of a parallelogram is 90 degrees.We can simply use the area of the triangle formula from the trigonometry concept for this case. The area of a parallelogram can also be calculated without the height if the length of adjacent sides and the angle between them are known to us. Solution: Given, length of base = 10 cm and height = 8 cmĪs per the formula, Area = 10 × 8 = 80 cm 2 Parallelogram Area Using Lengths of Sides Suppose 'a' and 'b' are the set of parallel sides of a parallelogram and 'h' is the height (which is the perpendicular distance between 'a' and 'b'), then the area of a parallelogram is given by:Įxample: If the base of a parallelogram is equal to 10 cm and the height is 8 cm, then find its area. if its two diagonals along with any of their intersecting angles are known.if the length of the adjacent sides along with the angle between them is known.

The parallelogram area can be calculated in each of the following cases: How to Calculate the Area of a Parallelogram? Also, the base and height of the parallelogram are equal to the length and breadth of the rectangle respectively.Īrea of Parallelogram = Base × Height (which is nothing but length × width of the rectangle).

Step IV: Paste the triangular portion (PSE) on the white chart joining sides RQ and SP.Īfter doing this activity, we observed that the area of a rectangle is equal to the area of a parallelogram.

Step III: Paste the remaining portion (EQRS) on a white chart.

Step II: Cut the triangular portion (PSE).

Step I: Draw a parallelogram (PQRS) with altitude (SE) on a cardboard and cut it.

Let's do an activity to understand the area of a parallelogram.

Thus, the area of the given parallelogram is base times the altitude. Note that we got the same answer using both methods. By counting the squares, we get:Īrea of the parallelogram = Side × height = 5 × 4 = 20 unit 2 Now, we will calculate the area of parallelogram by two methods: (i) By counting squares (ii) By using formulaĪrea of Parallelogram by Counting Squares:Īrea of the parallelogram = 16 + (1/2) × 8 = 16 + 4 = 20 unit 2Īlso, we observe in the figure that ST ⊥ PQ. Using grid paper, let us find its area by counting the squares. Let us analyze the above formula using an example. The formula to calculate the area of a parallelogram can thus be given as,Īrea of parallelogram = b × h square units The base and altitude of a parallelogram are perpendicular to each other as shown in the following figure. The area of a parallelogram can be calculated by multiplying its base by the altitude.

Sam rotated parallelogram abcd 180Â°