Unlocking the Mystery: Formula for Parallelogram Area

In English, a parallelogram is referred to as a Parallelogram, a quadrilateral with two pairs of parallel and equal-length sides. For a more comprehensive understanding, refer to the Wikipedia article on parallelograms. The formula for calculating the area of a parallelogram is relatively simple and finds widespread application in practical measurements and computations.

Unlocking the Mystery: Formula for Parallelogram Area

1. How to Calculate the Area of a Parallelogram: What's the Secret?

The area of a parallelogram is calculated by multiplying the height and the length of the base corresponding to the height.

- General Formula: S = a x h

Where:
- S is the symbol for area
- a is the base length corresponding to the height

- h is the height
- Area unit: square meters (m²)

2. Exercise: Calculating the Area of a Parallelogram

Exercise 1. Find the area of the parallelogram given:

a) base length a = 7 cm, height h = 4 cm
b) base length a = 3.41 dm, height h = 2.5 dm
c) base length a = 5/2 m, height h = 3/2 m
d) base length a = 4 m, height h = 20 dm

Solution:

Apply the formula for calculating the area of a parallelogram: S = a x h.
a. S = 7 x 4 = 28cm².
b. S = 3.41 x 2.5 = 8.525 dm².
c. S = 5/2 x 3/2 = 15/4m². 
d. Convert 4m to 40dm, so S = 40 x 20 = 800dm². 

Exercise 2. A field in the shape of a parallelogram has a height of 60 m, and the length of the base is three times the height. Calculate the area of this field.

Solution:

Length = 3 times the height = 3 x 60 = 180m
The area of the field is S = 60 x 180 = 10800m².

Exercise 3. A parallelogram-shaped aluminum piece has a height of 7 cm, and the length of the base is 1.5 dm. Calculate the area of this aluminum piece.

Solution:

Convert 7cm to 0.7dm.
Applying the formula, we have the area of the parallelogram as S = 0.7 x 1.5 = 1.05dm².

3. Tips for Memorizing the Area of a Parallelogram

Poem about Calculating Areas

Parallelogram area never goes wrong
Height times base, everyone can sing along.

Or:

Area of a parallelogram
Height times base, it's that simple, no need to roam.

Easy Tip:

To find the area of a parallelogram
Multiply the height by the base, that's the charm.

To find the area of a square
Multiply the side, a simple affair.
For the rectangle, make sure
Multiply length and width, that's the cure.

To find the area of a trapezoid
Add the big base and small, don't avoid.
Then multiply by the height's role
Divide by two, that's the whole goal.

The formula for calculating the trapezoid area is a crucial piece of knowledge that students are keen on mastering. It equips them to solve various geometry-related exercises with ease.