Calculating the area of a parallelogram with known side lengths

As you may know, to calculate the area of a parallelogram, you need to determine both the height and the base corresponding to it. But is it possible to find the area of a parallelogram when only two sides are given? Join us in this article to seek the solution to the problem of calculating the area of a parallelogram given two sides.

Calculating the area of a parallelogram when given two sides

Can you calculate the area of a parallelogram given the lengths of two sides?

- In reality, when only the lengths of two sides of a parallelogram are known, it will be quite challenging to calculate its area because there is insufficient information. Additional conditions are needed, such as the length of the height, the angle formed by the two sides, etc.

* Consider problem 1 : A parallelogram has two sides measuring 7 cm and 5 cm, respectively, and one of its altitudes has a length of 4 cm. Calculate the area of this parallelogram.

Solution Guide:

- Case 1: Assuming the height corresponds to the side of 5 cm:

=> Area = 5 x 4 = 20 (cm²)

- Case 2: Assuming the height corresponds to the side of 7 cm:

=> Area = 7 x 4 = 28 (cm²)

Similar Exercise:

1. Calculate the area of a parallelogram knowing the lengths of two sides are 3.5 cm and 6.12 cm, and one of the altitudes has a length of 5 cm.

2. Find the area of a parallelogram with two sides measuring 4/3 dm and 5/2 dm, and one of the altitudes has a length of 2.1 dm.

* Consider problem 2: Find the area of parallelogram ABCD given two sides are 12 cm and 15 cm, and the angle between them is 110 degrees.

Solution Guide: Assume AB = 12 cm, AD = 15 cm, angle A = 110 degrees.

As per the problem, since ABCD is a parallelogram, we have:

AD // BC => angle A + angle B = 180 degrees (due to alternate angles)

=> angle B = 180 - 110 = 70 degrees

Draw AH perpendicular to side BC, considering right triangle ABH:

AH = AB . sinB = 12 . sin70 = 11.2 (cm)

Also, AD = BC = 15 cm (since ABCD is a parallelogram)

=> SABCD = AH. BC = 11.2 x 15 = 168 (cm²)

Characteristics of the sides of a parallelogram

- The opposite sides of a parallelogram are parallel and equal in length.

- Given the length of any two sides, we can calculate the perimeter of the parallelogram using the formula: P = (a + b) x 2

Where:

P is the abbreviation for the perimeter of a parallelogram

a, b represent any two sides

- A trapezoid with two equal-length bases is a parallelogram.

A parallelogram is a relatively simple geometric shape, so you can easily remember the formulas for finding its perimeter or area. When encountering a problem asking to find the area of a parallelogram given two sides, make sure to read the problem carefully and analyze it thoroughly to find a reasonable solution.

In addition, you can explore more exercises on finding the area of a parallelogram given specific conditions, such as finding the area of a parallelogram given two diagonals. This is also a common type of problem you may encounter.