Parallelogram Formula

Example 1

Given a parallelogram with base *b = 4 units* and altitude *h = 3 units*, calculate the area and perimeter of the parallelogram.

1. Calculate the area:

A = 4 \times 3 = 12 square units

Therefore, the area of the parallelogram is *12 square units*.

2. Calculate the perimeter (assume all sides are equal):

P = 2 \times (4 + 4) = 16 units

Therefore, the perimeter of the parallelogram is *16 units*.

Example 2

Question: Given a parallelogram with sides of length 5 cm and 8 cm, and an angle of 60 degrees between these sides, find the area of the parallelogram.

Solution:

\text{Area of a parallelogram} = \text{base} \times \text{height}
= 8 \times 5 \times \sin(60^\circ)
= 8 \times 5 \times \frac{\sqrt{3}}{2}
= 20\sqrt{3} square cm

Example 3

Question: The diagonals of a parallelogram are 10 cm and 12 cm in length. If the angle between the diagonals is 45 degrees, calculate the area of the parallelogram.

Solution:

\text{Area of a parallelogram} = \frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 \times \sin(45^\circ)
= \frac{1}{2} \times 10 \times 12 \times \sin(45^\circ)
= \frac{1}{2} \times 10 \times 12 \times \frac{\sqrt{2}}{2}
= 60\sqrt{2} square cm

Example 4

Question: If the base of a parallelogram is 6 cm and the height is 4 cm, find the area of the parallelogram.

Solution:

\text{Area of a parallelogram} = \text{base} \times \text{height}
= 6 \times 4
= 24 square cm

Example 5

Question: The area of a parallelogram is 72 square units and its base is 9 units long. Find the height of the parallelogram.

Solution:

Let the height of the parallelogram be h. From the given information, we have:
72 = 9 \times h
h = \frac{72}{9}
h = 8 units

Example 6

Question: If the area of a parallelogram is 48 cm squared and its height is 6 cm, calculate the length of its base.

Solution:

Let the length of the base of the parallelogram be b. From the given information, we have:
48 = b \times 6
b = \frac{48}{6}
b = 8 cm