Parallelogram Properties, Area, and Perimeter

Parallelogram

Definition

In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.

Properties

A few notable properties of a parallelogram include:

• The opposed sides of a parallelogram are parallel. For example, PQ is parallel to RT, and PR is parallel to QT.
• The opposed sides of a parallelogram are equal in length. For example, PQ equals RT, and PR equals QT.
• The opposed angles of a parallelogram are equal in measure. For example, ∠P = ∠T, and ∠Q = ∠R.
• The diagonals of a parallelogram bisect each other. For example, line RE is congruent to line EQ, and line PE is congruent to line ET.
• Diagonal lines divide the parallelogram into two congruent triangles. For instance, ΔRPQ is congruent to ΔQTR.

Area

The area of a parallelogram can be found by multiplying the base (b) by the height (h):

[K = bh]

where (K) represents the area, (b) denotes the base, and (h) signifies the height.

For example, consider a parallelogram with a base of 8 centimeters (cm) and a height of 4 cm. Using the formula above, we can calculate the area as follows:

[K = bh = 8cm \times 4cm = 32~cm^2]

This indicates that the area enclosed within the parallelogram is 32 square centimeters.

Perimeter

Parallel to the area formula, the perimeter of a parallelogram can be computed by adding up all the side lengths:

[P = 2(a + b)]

Where (P) is the perimeter, (a) represents the first side length, and (b) denotes the second side length.

For instance, take a parallelogram with side lengths a = 5 cm and b = 4 cm. Following the formula above, we obtain:

[P = 2(5cm + 4cm) = 14~cm]

Thus, the perimeter of the parallelogram amounts to 14 centimeters.

Learn about the definition, properties, area calculation, and perimeter calculation of parallelograms in geometry. Understand concepts such as parallel sides, equal side lengths, equal angles, diagonal properties, and the formulas for calculating area and perimeter.