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.