# Parallel space law ribs ## Contents

• 1 Overview of the ribs parallel area
• 2 laws calculate the area of ​​a parallelogram
• 3 Examples of parallel space calculation ribs
• 4 References

## Overview of a parallel area of ​​ribs

It features a parallelogram that has four sides, each two ribs opposite each parallel and equal in length, can be defined as the area in general as a vacuum amount inside form a two-dimensional, and Klzlk case for space parallelogram (in English: Area of ​​Parallelogram) that can be calculated simply by multiplying the length of its base, rising. 

## Calculate the area laws parallelogram

It can be found in an area of ​​parallelogram by using one of the following laws:

• Using the length of the base, and height, so as follows:  parallel space along the base = Ribs × height, symbols: m = b × p; Where: B: the length of the base parallelogram. P: high parallelogram. For example, if there was a parallelogram along the base of 5 cm, and a height of 3 cm, the area according to the previous law are: parallelogram area = length of the base height × 5 × 3 = = 15 cm².
• Parallel space = Ribs × length of the base height, and symbols: m = b × p; Where: B: the length of the base parallelogram. P: high parallelogram.
• B: the length of the base parallelogram.
• P: high parallelogram.
• For example, if there was a parallelogram along the base of 5 cm, and a height of 3 cm, the area according to the previous law are: parallelogram area = length of the base height × 5 × 3 = = 15 cm².
• Using the length of two ribs, and the angle confined between them, so as follows: Parallel ribs area = length of the base × length of the lateral rib × Ga the angle between them, and symbols: M = A × B × Ga (x); Where: A: rib along the side of the parallelogram. B: the length of parallel ribs base. Q: the angle between the base and the lateral rib. M: parallelogram space. For example, if there was a parallelogram along one of the ribs 3 cm, and the other side of 4 cm, and measuring all angles 90 degrees, the area in accordance with the law, the former is: parallelogram area = length of the base × length of the lateral rib × Ga the angle between them = 3 × 4 × Ga ( 90) = 12 cm².
• Parallel ribs area = length of the base × length of the lateral rib × Ga the angle between them, and symbols: M = A × B × Ga (x); Where: A: rib along the side of the parallelogram. B: the length of parallel ribs base. Q: the angle between the base and the lateral rib. M: parallelogram space.
• A: rib along the side of the parallelogram.
• B: the length of parallel ribs base.
• Q: the angle between the base and the lateral rib.
• M: parallelogram space.
• For example, if there was a parallelogram along one of the ribs 3 cm, and the other side of 4 cm, and measuring all angles 90 degrees, the area in accordance with the law, the former is: parallelogram area = length of the base × length of the lateral rib × Ga the angle between them = 3 × 4 × Ga ( 90) = 12 cm².
• Using the length of the country, and the angle confined between them: the parallelogram tar intersect to form between the amount of angle (r), and the other of (p), and to calculate the parallel area of ​​the ribs using the length of the diameters are used the law as follows:  parallel space rib = ½ × length of the first diameter × diameter × length of the second Ga (the angle between them), and symbols: m = ½ × s × × for Ja (r or p); Where: M: parallelogram space. S: length of the first diameter. For: the length of the second diameter. P, p: angles confined between the two countries.
• Parallelogram area = ½ × length of the first diameter × diameter × length of the second Ga (corner confined between them), and symbols: m = ½ × s × × for Ja (r or p); Where: M: parallelogram space. S: length of the first diameter. For: the length of the second diameter. P, p: angles confined between the two countries.
• M: parallelogram space.
• S: length of the first diameter.
• For: the length of the second diameter.
• P, p: angles confined between the two countries.

## Examples of parallel space calculation ribs

• The first example: the length of the parallel sides of the base 1.5 cm, and a height of 1 cm, what is the area?  Solution: application of space law parallelogram = length of the base × height, that produces: parallelogram = 1.5 × 1 = 1.5 cm² space.
• Solution: application of space law parallelogram = length of the base × height, that produces: parallelogram = 1.5 × 1 = 1.5 cm² space.
• Example Two: parallel sides of the length of the base 2 O, and the height S², what is the area?  Solution: application of space law parallelogram = length of the base × height, produces that: an area of ​​parallelogram = 2 x × x = 2 S³ cm².
• Solution: application of space law parallelogram = length of the base × height, produces that: an area of ​​parallelogram = 2 x × x = 2 S³ cm².
• Third example: parallelogram father c d, base (b c) equal to 22 cm, in which the column (DU) plopped corner d towards the base (b c), and length (c) equal to 12 cm, rib (d c) 18 cm, the very area.  solution: To resolve this question is the following steps: Calculate the height of the application of space law parallelogram which is equal to the base length × height using the Pythagorean theorem, which states that: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², so the 18² = (first rib (dU)) ² + 12², and it (du), a height = 180√sm. Application Area Code: space parallelogram = length of the base × height = 22 × 180√ = 295.1 cm. Can also solve the question in another way: is calculating the angle between the base and lateral rib, by using the cosine angle law, a cos (x) = adjacent / tendon, which: cos (x) = 12/18 = 0.666, and from Q = 48.18 degrees, then the application of the law: a parallel area of ​​ribs = length of the base length of the lateral rib × × Ga confined between the angle = 22 × 18 × Ga (48.18) = 295.1 cm
• Solution: To resolve this question is the following steps:
• Calculate the height of the application of space law parallelogram which is equal to the base length × height using the Pythagorean theorem, which states that: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², so the 18² = (first rib (dU)) ² + 12², and it (du), a height = 180√sm.
• Application Area Code: space parallelogram = length of the base × height = 22 × 180√ = 295.1 cm.
• Can also solve the question in another way: is calculating the angle between the base and lateral rib, by using the cosine angle law, a cos (x) = adjacent / tendon, which: cos (x) = 12/18 = 0.666, and from Q = 48.18 degrees, then the application of the law: a parallel area of ​​ribs = length of the base length of the lateral rib × × Ga confined between the angle = 22 × 18 × Ga (48.18) = 295.1 cm
• Example IV: parallelogram area of ​​6 square units, and the length of its base Q, and the height x + 1, what is the length of its base, and the height?  Solution: application of space law parallelogram = length of the base × height, produces that: 6 = (o) (x + 1), and from 6 = S² + x, and to solve this equation, find the value of x, through analysis to (x - 2) (x + 3) = 6, the values ​​of x equals x = 2, o = -3 , excluding the negative value of the base that produces the length = 2 cm, and the height equals x + = 1 + 2 = 1 3 cm.
• Solution: application of space law parallelogram = length of the base × height, produces that: 6 = (x) (x + 1), and from 6 = S² + x, and to solve this equation, find the value of x, through analysis to (x - 2 ) (x + 3) = 6, the values ​​of x equals x = 2, o = 3, excluding the negative value of the base that produces the length = 2 cm, and the height equals x + = 1 + 2 = 1 3 cm.
• Example V: What are the parallelogram area that the length of base 8 cm, and a height of 11 cm?  Solution: application of space law parallelogram = length of the base × height, produces that: an area parallelogram 11 × 8 = = 88 cm².
• Solution: application of space law parallelogram = length of the base × height, produces that: an area of ​​parallelogram = 11 × 8 = 88 cm².
• Example VI: If the length of the parallel base Ribs is equivalent to three times the height and area of ​​192 cm², what is the length of its base, and the height?  Solution: Using space law parallelogram = length of the base × height, assuming that the base length is x, and the height is 3 x , it produces that: an area of ​​parallelogram = 3 x × x = 192, and from x = 8 cm, the length of the base, and the height is a 3 x 3 × 8 = = 24 cm².
• Solution: Using space law parallelogram = length of the base × height, assuming that the base length is x, and the height is 3 x, produces that: an area of ​​parallelogram = 3 x × x = 192, and from x = 8 cm, which is the base length, the height is a 3 x = 3 × 8 = 24 cm².
• Seventh: parallelogram father c d, base (b c example) equal to 15 cm, in which the column (DU) plopped corner d towards the base (b c), and length (c) equal to 5 cm, rib (c d) 13 cm, the very area.  solution: To resolve this question is the following steps: Calculate the height of the application of space law parallelogram which is an area of ​​parallelogram = length of the base × height using the Pythagorean theorem, namely: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², thus, 13² = (first rib (dU)) ² + 5², and it (du), a height = 12 cm. Application Area Code: space parallelogram = length of the base × height = 15 × 12 = 180 cm.
• Solution: To resolve this question is the following steps:
• Calculate the height of the application of space law parallelogram which is an area of ​​parallelogram = length of the base × height using the Pythagorean theorem, namely: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², thus, 13² = (first rib (dU)) ² + 5², and it (du), a height = 12 cm.
• Application Area Code: space parallelogram = length of the base × height = 15 × 12 = 180 cm.
• Eighth example: parallelogram along the base of 12 cm, and the length of the rib side 20 cm, and measuring the angle between the rib and the base = 60 degrees, calculate the area.  The solution: application of the law: a parallel area of ​​ribs = length of the base × length of the lateral rib × Ga the angle between them = 12 × 20 × Ja (60) = 207.8 cm².
• Solution: applying the law: an area of ​​parallelogram = the base length × length of the lateral rib × Ga between the angle = 12 × 20 × Ja (60) = 207.8 cm².
• Ninth example: parallelogram father c d, base (b c) equal to 23 cm, in which the column (DU) plopped corner d towards the base (b c), and length (c) equal to 5 cm, and the angle c = 45 degrees, very area. [ 8] solution: Height (de account) using the law under the angle = opposite / next door, and it tan (45) = height / 5, and from the height = 5 cm. Application Area Code: space parallelogram = length of the base × height = 23 × 5 = 115 cm².
• The solution:
• Height (de account) using the law under the angle = opposite / next door, and it tan (45) = height / 5, and from the height = 5 cm.
• Application Area Code: space parallelogram = length of the base × height = 23 × 5 = 115 cm².
• Example X: parallelogram area of ​​152 cm², and the length of its base 9 cm, what is the height?  Solution: application of space law parallelogram = length of the base × height, produces that: 152 = 9 × height, and from Height = 153/9 = 17 cm.
• Solution: application of space law parallelogram = length of the base × height, results that: 152 = 9 × height, and from Height = 153/9 = 17 cm.
• Example atheist ten: parallelogram father c d, base (b c) equal to 21 cm, in which the column (DU) plopped corner d towards the base (b c), and length (c) equal to 8 cm, rib (d c) = 17 cm, grandfather area.  the solution: To resolve this question is the following steps: Calculate the angle between the lateral rib and the base by using a pocket law fully angle = adjacent / plugged in, and it cos (x) = 8/17 = 0.47, and from Q = 61.9 degrees. Law enforcement: parallelogram space = length of the base × length of the lateral rib × Ga between the angle = 21 × 17 × Ga (61.9) = 315 cm². Can also be the question resolved in another way it is to calculate the height by the Pythagorean theorem, the result that: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², so the 17² = (rib The first (dU)) ² + 8², and it (du), a height = 15 cm, and then apply the law: a parallel area of ​​ribs = length of the base × height = 21 × 15 = 315 cm².
• Solution: To resolve this question is the following steps:
• Calculate the angle between the lateral rib and the base by using a pocket law fully angle = adjacent / plugged in, and it cos (x) = 8/17 = 0.47, and from Q = 61.9 degrees.
• Law enforcement: parallelogram space = length of the base × length of the lateral rib × Ga between the angle = 21 × 17 × Ga (61.9) = 315 cm².
• Can also be the question resolved in another way it is to calculate the height by the Pythagorean theorem, the result that: (plugged in (c d)) ² = (first rib (DU)) ² + (second rib (c)) ², so the 17² = (rib The first (dU)) ² + 8², and it (du), a height = 15 cm, and then apply the law: a parallel area of ​​ribs = length of the base × height = 21 × 15 = 315 cm².

## References

• ↑ "How Area Formulas of Triangles, Parallelograms & Trapezoids Relate", study.com, Retrieved 24-3-2020. Edited.
• ^ أ ب ت ث "Area of Parallelogram", byjus.com, Retrieved 24-3-2020. Edited.
• ^ أ ب "How to find the area of a parallelogram", www.varsitytutors.com, Retrieved 24-3-2020. Edited.
• ↑ "How to find the area of a parallelogram", www.varsitytutors.com, Retrieved 24-3-2020. Edited.
• ↑ "How to find the area of a parallelogram", www.varsitytutors.com, Retrieved 24-3-2020. Edited.
• ↑ " Areas of Parallelograms and Triangles", 1.cdn.edl.io, Retrieved 24-3-2020(page 1). Edited.
• ↑ " Areas of Parallelograms and Triangles", 1.cdn.edl.io, Retrieved 24-3-2020 (page 2). Edited.
• ↑ "Areas of Parallelograms and Triangles", 1.cdn.edl.io, Retrieved 24-3-2020 (page 3). Edited.
• ↑ "Areas of Parallelograms and Triangles", 1.cdn.edl.io, Retrieved 24-3-2020 (page 6). Edited.
• ↑ "Areas of Parallelograms and Triangles", 1.cdn.edl.io, Retrieved 24-3-2020 (page 8). Edited.

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