How To Find The Sides Of A Parallelogram

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What if yous know the area of the parallelogram, can you find the meridian?

How practise y'all find the peak of a Parallelogram if it is not given?

The formula for finding the area of a parallelogram is base times the height , only there is a slight twist.

The tiptop is non the side length similar you might use in a rectangle, only instead information technology is the altitude.

The elevation (altitude) is found past drawing a perpendicular line from the base to the highest bespeak on the shape.

The Pythagorean Theorem tin can also be used to observe the height of the parallelogram if height is not given. In society to use this method you demand to know the base length of the right triangle. In the problem below information technology is the distance from a to b.

In one case the elevation is calculated you tin utilise the area of a parallelogram formula,

base * height

Discover the area of a parallelogram with a base of 12 units and a slant height of 5 units

Stride 1. Observe the pinnacle (altitude) using the Pythagorean Theorem.

When using the Pythagorean Theorem the C^2 is always the hypotenuse of the right triangle.

a^2 +b^ii =c^2

3^2 + h^two =5^2 (see the right triangle)

nine+ h^2 = 25

h^2 = 16

Take the square root each side

√h^2 = √xvi

height of parallelogram =4

Pace 2. At present utilise, surface area= base * height

A=12 * four = 48 units^two

Footstep 2. The side of the parallelogram becomes the hypotenuse in the right triangle

Therefore 6=2x

Divide both sides past 2

6/2 = 2x/10

10=3

Step three. Now that I know x I can observe the summit using thirty-60-90 rules. The parallelogram summit is the length of the long leg.

Long leg=three√ten

3√3

Step 4. Use surface area equals base of operations * meridian or A =b*h

ten * 3√3 = 30√3 = 51.9615 units^2 area of parallelogram

Expanse parallelogram without top given

a b c

3 9

One tin can calculate the area of a parallelogram using vectors.

The surface area of a parallelogram is equal to the magnitude of the cross product.

Follow the link for a very helpful video that explains how to detect the expanse from 2 vectors

Parallelogram surface area from ii vectors

Area parallelogram given diagonals

The diagonals of a parallelogram do not define the expanse of a parallelogram and then one tin not use: ½ d1*d2 again do not use ½ d1 * d2

Common Core Standard six.One thousand.1 , 7.G.6 6th Grade Math 7th Course Math

Problem one. What is the area of a parallelogram with a base of 8 units and sides of 5 units and a height of 4 units?

This problem is straight forward because pinnacle is given. Merely employ base of operations times height

Step one. Multiply the base of viii units times the height of 4 units.

Step 2. viii*4 = 32 units squared

Trouble 2. What is the area of a parallelogram that has a side of 6 units, a base of 10 units, and an bending measure out of 60 degrees?

This trouble is a footling catchy considering the height is not given. Because the parallelogram has an bending of threescore degrees you can create a 30-threescore-90 triangle to detect the summit.

Step 1. Find the altitude. If you draw a vertex direct down it creates a triangle. Run across moving picture below. The triangle is a 30-threescore-90 triangle. I can utilise the 30-60-90 rules to find the height of the parallelogram.

The rules of a 30-60-90 are every bit follows:

parallelogram 6x10

30 60 90 triangle

parallelogram 6x10

The formula for area of a Parallelogram equals b x h ( base x height )

parallelogram 5x8

Area of a Parallelogram Formula

There are at least two means to observe the height (altitude) of a parallelogram.

Method one: Employ the Pythagorean Theorem and the side length of the parallelogram and the distance of the base to the height.

Method two:If you lot are given an angle measure that creates a special right triangle you can use the rules of the special right triangle to find the pinnacle.

parallelogram forms a right triangle