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Area Of Parallelogram: Formula, How To Calculate Area, Methods, Examples

Area Of Parallelogram

To find the Area Of A Parallelogram, multiply the base by the height. A parallelogram is a 4-sided shape formed by two pairs of parallel lines. Opposite sides are equal in length and opposite angles are equal in measure.

Students who are looking for the area of parallelogram formula and how to Calculate Area, they can get all the details of methods as well as examples regarding this through below section of this page which is well created by the team of recruitmentresult.com.

Area Of Parallelogram

The total space inside the boundary of the parallelogram is called as the area of the parallelogram. The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

In a parallelogram, the opposite sides are equal to each other and the opposite angles are also equal to each other. The sum of all the interior angles of a parallelogram is 3600.

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Formula For Area Of A Parallelogram Is

A = b x h

Where,

A- Area in square meter.

B- Base in meter.

H- Height in meter.

The base and height of a parallelogram must be perpendicular. However, the lateral sides (L) of a parallelogram are not perpendicular to the base.

Perimeter Of Parallelogram = 2(AB + BC)

                                      = 2 × (Sum of adjacent sides)

How To Find Area Of Right Angled Triangle: Formula with Examples

Labeling Your Measurements

In order to find the area of a parallelogram, we need to label our measurements. There are only two measurements that we need to be concerned about. If our parallelogram is sitting on a flat surface, the first measurement we need is the length of the bottom side. This we can label with a b for base. We call this the base because it is the bottom of the parallelogram.

The next measurement we need is the height of the parallelogram. This is the straight up and down measurement from the bottom to the top. We can label this measurement h for height. Note that this is not how long the leaning sides are, but the distance between the bottom side and the top side.

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

Area Of Parallelogram Examples

Question: Find the area of a parallelogram with a base of 28 inch and a height of 24 inch with a lateral side length of 31 inch.

Solution:

A = b x h

= 28 x 24

= 672 inch square

Question: The base of a parallelogram is 15 cm and the height is 10cm. What are the area and perimeter of this parallelogram?

Solution: We know the area is

A = bh
A = 15 * 10
A = 150cm2

We do not have any information about the left and right sides.

Thus, we cannot determine the perimeter.

Want to Know? How to Find Area of Square

Question: A parallelogram has a base of 3x, a height of x, and the other side of the parallelogram (not the base) is 2x. If the area of this parallelogram is 15, what is its perimeter?

Solution:

Notice in the diagram that we know enough information to formulate an equation for the area of the parallelogram

A = bh = (3x)x = 3×2
A = 15

3×2 = 15
x2 = 5

x = √5

Since x = √5, we know the height h = √5, the base b = 3x = x√5 and the other side is 2x = 2√5.

The perimeter is the sum of the four sides, namely the two bases and two other sides.

Perimeter = 2 * (3 * √5) + 2 * (2 *√5 ) = 10√5

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Question: A parallelogram is 3 yards long. The height, measured perpendicular to this side, is 1.5 yards. What is the area?

Solution: Since they are perpendicular, the side measurement and the height can be used in the formula.

A = 3 * 1.5

A = 4.5 square yards.

Method 1: Finding the Area of Two-Dimensional Parallelograms

a) Multiply the base of the parallelogram by the height to find the area: If your problem gives you a measurement of the base and height of a parallelogram, simply multiply them to get your area. For example, if the base is 5, and the height 3, then your area is 15in2 since 5*3=15

The base is the length of the long, flat side on the bottom.

The height is the distance from the base straight up to its parallel side.

Which side is the base and which is height is entirely up to you — you could rotate any parallelogram to make any side the bottom and still get the same final answer.

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b) Measure or record the length of the long, flat side, or base: A parallelogram consists of two sets of parallel lines, and one side is usually presented as the “bottom,” making two of your sides appear flat. Measure this flat edge and write it down as the base, or “B.”

For this example, assume the base has a length of 10cm.

c) Draw a line straight up from the base to it’s parallel side: This must be a 90-degree angle so that your measurement for the height is perpendicular to the base. The easiest way to get this is to measure from the bottom corner straight up, using a ruler to line everything up.

You do not measure the height by measuring the slanted sides.

d) Measure the distance between your base and the top of the parallelogram for height: As long as your line is perpendicular (at a 90-degree angle to the base, this is your height. Write it down for “H.”

For this example, assume that the height is 5cm.

The height may be drawn outside of the parallelogram.

e) Multiply the base by the height to find the area: Once you’ve got your two measurements, simply add them to the equation {A=B*H} where A stands for your area. Finishing the work:

  • A=B*H
    • B= 10cm; H= 5cm
  • A= 10cm*5cm
  • Area of Parallelogram= 50cm2

How to Find: Area Of A Trapezium

Method 2: Finding the Surface Area Parallelepipeds

a) Treat a three-dimensional parallelogram just link any other surface area problem: Three-dimensional parallelograms also called “parallelepipeds,” are as easy to solve as any other 3D rectangle. Simply find your three measurements– length (l), height (h), and width (w), and then input them into the following formula:

Lateral Surface Area = 2(lh+lw+hw)

b) Find length and height of one side of the prism: If you’ve got a rectangular solid (a math term for a box) where one of the sides is a parallelogram, you can measure the length and height the exact same way as when you measured the length and height for a 2D parallelogram. Remember that these two measurements must be perpendicular, meaning they must form a right-angle, for the measurements to be correct. When done, write down these measurements as length and height.

Remember — the height is not the length of the diagonal side — it is the distance between the side you measured for length and its parallel side.

For this example, say that l=6;h=4, and that you measured in inches.

Check Formula to Find: Area of Quadrilateral

c) Find the width by measuring a side that is moving away from your length and height sides: This is the last distance you haven’t measured. Just make sure that you don’t re-measure a side that is parallel to your length or height — the width should be a distinct measurement. You should be able to take all three measurements from the exact same point, with each line perpendicular to each other line.

For this example, say that the width is {w=5in}

d) Add all three of your measurements to the formula to get your surface area: Once you’ve measured all three sides, or if the problem gives them to you. Then you’re ready to finally solve. Simply input it all into the formula:

  • Lateral Surface Area= 2(lh+lw+hw)

l=6in; h=4in; w=5in

  • Lateral Surface Area =2(6*4+6*5+4*5)
  • Lateral Surface Area =2(24+30+20)
  • Lateral Surface Area =2(74)
  • Lateral Surface Area =148in2

Must Know? Area of Hexagon

Final Words:

We hope that you are satisfied with the details of how to find area of rhombus and what is the formula of area of rhombus provided on this page. Still if you have any queries or doubts regarding this, then you may type your comment in below comment box. Our experts will soon your queries.

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