Finding the area of ​​a parallelogram: formula and examples

Parallelogram is a geometric figure; a quadrilateral whose opposite sides are equal and parallel.

Area formula

Side length and height

The area of ​​a parallelogram (S) is equal to the product of the length of its side and the height drawn to it:

S = a ⋅ h

On two sides and the angle between them

The area of ​​a parallelogram is found by multiplying the lengths of its two sides and the sine of the angle between them:

S = a ⋅ b ⋅ sin α

Two diagonals and the angle between them

The area of ​​a parallelogram is equal to one second of the product of the lengths of its diagonals multiplied by the sine of the angle between them:

S = ¹/₂ ⋅ d ₁ ⋅ d ₂ ⋅ sin a

Examples of tasks

Task 1

Find the area of ​​a parallelogram if its side length is 7 cm and its height is 4 cm.

Decision:

We use the first formula, which uses the values ​​u4bu7bknown to us according to the conditions for setting: S u28d XNUMX cm * XNUMX cm uXNUMXd XNUMX cm².

Task 2

Find the area of ​​a parallelogram if its sides are 6 and 8 cm and the angle between them is 30°.

Decision:

Let’s apply the second formula discussed above: S = 6 cm * 8 cm * sin 30° = 24 cm².

Task 3

Find the area of ​​a parallelogram with diagonals 4 and 6 cm. The angle between them is 90°.

Decision:

Let’s use the formula in which the diagonals appear: S u1d 2/4 * 6 cm * 90 cm * sin 12 ° uXNUMXd XNUMX cm².