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Grasping the formula for calculating the perimeter of a parallelogram not only aids students in solving shape-related math problems but also teaches them how to apply it in calculating perimeters and areas of shapes in specialized fields like design and construction in the future.
Learn the formula and method to calculate the perimeter of a parallelogram.
Calculating the perimeter of a parallelogram
1. Formula for calculating the perimeter of a parallelogram
Deriving from the definitions of parallelograms in the Grade 4 textbooks, we derive the formula for calculating the perimeter of a parallelogram as follows:
C = (a + b) x 2
Where:
C represents the perimeter of the parallelogram
a, b are any two arbitrary base sides of the parallelogram
Therefore, we can also easily find a way to calculate half the perimeter of a parallelogram using the formula: 1/2 C = a + b
2. Exploring More about the Concept and Characteristics of Parallelograms
- Concept of Parallelogram: A parallelogram is a special case of a trapezoid with pairs of opposite sides being parallel and equal in length, opposite angles being equal, and diagonals intersecting at their midpoints.
- Theory of Parallelogram Perimeter: The perimeter of a parallelogram equals twice the sum of any adjacent pair. In simpler terms, the perimeter of a parallelogram equals the sum of all four sides in that parallelogram.
For a deeper understanding of the concept, identifying characteristics, formulas for calculating the perimeter and area of a parallelogram, you can explore the knowledge on Wiki by clicking on this link
Images, formulas for calculating the perimeter of a parallelogram in mathematics.
3. Exercises on Calculating the Perimeter of a Parallelogram
Case 1: Grade 4 Math - Calculating the Perimeter of a Parallelogram
Applying the rule for calculating the perimeter of a parallelogram in Grade 4, we have exercises ranging from basic to advanced as follows:
Exercise 1: Given a parallelogram ABCD with two sides a and b measuring 5 cm and 8 cm respectively. What is the perimeter of parallelogram ABCD?
Solution:
Applying the formula for calculating the perimeter of a parallelogram, we have:
C (ABCD) = (a +b) x 2 = (5+8) x 2 =13 x 2 = 26 cm
Answer: The perimeter of parallelogram ABCD is 26 cm
Exercise 2: Given a parallelogram with a perimeter of 480 cm, where one side of the base is 5 times the length of the other side. Calculate the lengths of the sides of this parallelogram.
Solution:
- We have half the perimeter of the parallelogram as: 480 : 2 = 240 (cm)
According to the data given in the problem, if one side is considered as 1 part, then the base side will be 5 parts. Therefore, we have:
+ The length of the other side of the parallelogram is: 240 : (5+1) = 40 (cm)
+ The length of the base side of the parallelogram is: 40 x 5 = 200 (cm)
Answer: The base side of the parallelogram has a length of 200cm, and the other side of the parallelogram has a length of 40cm
Case 2: Advanced Exercise on Calculating the Perimeter of a Parallelogram
Grade 4 exercises on calculating the perimeter of a parallelogram are not only about finding the perimeter and lengths of its sides but also involve calculating the area of the parallelogram. Specifically:
Exercise on calculating the area of a parallelogram:
A parallelogram has a base side of 50cm. It is then reduced by decreasing the base sides by 15 cm, resulting in a new parallelogram with an area smaller than the original area by 90 cm2. Calculate the area of the original parallelogram.
Solution:
Note: To solve this exercise, we need to know the formula for calculating the area of a parallelogram. Specifically:
Formula: S = a x h
Where:
a: Base side of the parallelogram.
h: Height (the perpendicular distance from the vertex to the base of a parallelogram):
Detailed Solution:
According to the given conditions, we have the following equations:
- The area of the original parallelogram is: S1 = 50 x h
- The area of the parallelogram after reducing the base side by 15cm is: S2 = 35 x h
Given that S1 = S2 + 90
Therefore, we have the equation as follows:
50 x h = 35 x h + 90
Solving the equation above, we get the result h = 6 cm
So, the area of the original parallelogram is: S1 = 6 x 50 = 300 (cm2)
Answer: The area of the original rectangle is 300 cm2
In this article, Mytour.vn has shared with you the formula for calculating the perimeter of a parallelogram and some exercises on calculating the perimeter of a parallelogram in Grade 4 from basic to advanced. For advanced exercises on calculating the perimeter of a parallelogram, you need to apply the knowledge you have learned and combine it with the relationship between the formulas for calculating the perimeter and area of geometric shapes to find the most accurate solution for your problem.
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Also, a special case of a trapezoid, a square trapezoid has a completely different rule for calculating the perimeter compared to a parallelogram. Parents and students also need to know how to calculate the perimeter of a square trapezoid for use when necessary.
