# canal24.info

A parallelogram is a quadrilateral made from two pairs of intersecting parallel lines. There are several rules involving:

Rule 2: Opposite Sides are Congruent Read more

You get 20-40 Free Gizmos to teach with See the full list. Access lesson materials for Free Gizmos. Teacher guides, lesson plans, and more. All other Gizmos are limited to a 5 Minute Preview Get a 5 Minute Preview of all other Gizmos. They can only be used for 5 minutes a day. This free app is a geometric calculator which is able to calculate area and volume. Area Calculator: You are able to calculate the area for the most important geometric figures. You can calculate the area of circle, ellipse, rectangle, square, trapezoid, triangle, parallelogram, rhombus, sector and triangle. Volume Calculator: You are able to calculate the volume for the most important.

Properties of parallelograms:

A classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral. Then ask the students to measure the angles, sides etc. of inscribed shape and use the measurements to classify the shape (parallelogram). Designed with Geometer's Sketchpad in mind .

Types of Parallelograms:

As the name suggests, a parallelogram is a quadrilateral formed by two pairs of parallel lines. It differs from rectangle in terms of measure of angles at the corners. In a parallelogram, the opposite sides are equal in length and opposite angles are equal in measure, while in a rectangle, all angles are 90 degrees.

In this article, you will learn how to calculate the area of a parallelogram using parallelogram area formula.

To find how its area different from other quadrilaterals and polygons, visit the previous articles.

## How to Find the Area of a Parallelogram?

The area of a parallelogram is the spaced enclosed by 2 pair of parallel lines. A rectangle and a parallelogram have similar properties, and therefore, the area of a parallelogram is equal to the area of a rectangle.

## Area of a Parallelogram Formula

Consider a parallelogram ABCD shown below. The area of the parallelogram is the space bounded by the sides AD, DC, CB and AB.

The area of parallelogram formula states;

Area of a parallelogram = base x height

A = (b * h) Sq. units

Where b = the base of a parallelogram and,

h = The altitude or the height of a parallelogram. The miracle & tragedy of the dionne quintuplets pdf free download.

The height or altitude of a parallel is the perpendicular line, (usually dotted) from the vertex of a parallelogram to any of the bases.

Example 1

Calculate the area of a parallelogram whose base is 10 centimeters and height is 8 centimeters.

Solution

A = (b * h) Sq. units.

A = (10 * 8)

A = 80 cm2

Example 2

Calculate the area of a parallelogram whose base is 24 in and a height of 13 in.

Solution

A = (b * h) Sq. units.

= (24 * 13) square inch.

= 312 square inches.

Example 3

If the base of a parallelogram is 4 times the height and the area is 676 cm², find the base and height of the parallelogram.

Solution

Let the height of the parallelogram = x

and the base = 4x

But, the area of a parallelogram = b * h

676 cm² = (4x * x) Sq. units

676 = 4x2

Divide both sides by 4 to get,

169 = x2

By finding the square root of both sides, we get,

x = 13.

Substitute.

Base = 4 * 13 = 52 cm

Height = 13 cm.

Therefore, the base and height of the parallelogram are 52 cm and 13 cm, respectively.

Apart from area of parallelogram formula, there area other formulas for calculating the area of a parallelogram.

Let’s take a look.

### How to find the area of a parallelogram without a height?

If the height of the parallelogram is unknown to us, then we can use trigonometry concept here to find its area.

Area = ab sine (α) =ab sine (β)

where a and b are the length of parallel sides and either β or α is the angle between the sides of the parallelogram.

Example 4

Find the area of a parallelogram if its two parallel sides are 80 cm and 40 cm and the angle between them is 56 degrees.

Solution

Let a = 80 cm and b = 40 cm.

The angle between a and b = 56 degrees.

Area = ab sine (α)

Substitute.

A = 80 × 40 sine (56)

A = 3,200 sine 56

A = 2,652.9 sq.cm.

Example 5

Calculate the angles between the two sides of a parallelogram, if its side lengths are 5 m and 9 m and the area of the parallelogram is 42.8 m2.

Solution

Area of a parallelogram = ab sine (α)

42.8 m2 = 9 * 5 sine (α)

42.8 = 45 sine (α)

Divide both sides by 45.

0.95111= sin (α)

α = sine-1 0.95111

α = 72°

But β + α = 180°

β = 180° – 72°

= 108°

Therefore, the angles between the two pairs of parallel sides of the parallel are; 108° and 72°.

Example 6

Calculate the height of a parallelogram whose parallel sides are 30 cm and 40 cm and the angle between these two sides is 36 degrees. Take the base of the parallelogram to be 40 cm.

Solution

Area = ab sine (α) = bh

30 * 40 sine (36) = 40 * h

1,200 sine (36) = 40 * h.

Divide both sides by 40.

h = (1200/40) sine 36

= 30 sine 36

h = 17.63 cm

So, the height of the parallelogram is 17.63 cm.

### How to find the area of a parallelogram using diagonals?

Suppose d1 and d2 are the diagonals the parallelogram ABCD, then the area of the parallelogram is given as,

A = ½ × d1 × d2 sine (β) = ½ × d1 × d2 sine (α)

Where β or α is angle of intersection of the diagonals d1 and d2.

Example 7

Calculate the area of a parallelogram whose diagonals are 18 cm and 15 cm and the angle of intersection between the diagonals is 43°.

Solution

Let d1 = 18 cm and d2 = 15 cm.

β = 43°.

A = ½ × d1 × d2 sine (β)

= ½ × 18 × 15 sine (43°)

= 135sine 43°

= 92.07 cm2

Therefore, the area of the parallelogram is 92.07 cm2.

Practice Questions

### Area Of Parallelograms Calculator

1. A flag has a base of 2.5 ft and a height of 4.5 ft. If the flag is parallelogram-shaped, find the area of the flag.
2. Consider a parallelogram which has an area twice the area of a triangle. If both of these shapes have a common base, what is the relation between their heights?