## What is the Area of a Parallelogram?

The area of a parallelogram is the region bounded by the parallelogram in a given two-dimension space. To recall, a parallelogram is a special type of quadrilateral which has four sides and the pair of opposite sides are parallel. In a parallelogram, the opposite sides are of equal length and opposite angles are of equal measures. Since the rectangle and the parallelogram have similar properties, the area of the rectangle is equal to the area of a parallelogram.

## Area of Parallelogram Formula

To find the area of the parallelogram, multiply the base of the perpendicular by its height. It should be noted that the base and the height of the parallelogram are perpendicular to each other whereas the lateral side of the parallelogram is not perpendicular to the base. Thus, a dotted line is drawn to represent the height.

Therefore,

Area = b × h Square units |

Where “b” is the base and “h” is the height of the parallelogram.

### How to Calculate the Area of Parallelograms?

The parallelogram area can be found by using its base and height. Apart from it, the area of a parallelogram can also be found if its two diagonals are known along with any of their intersecting angles, or if the length of the parallel sides are known along with any of the angles between the sides.

All Formulas to Calculate Area of a Parallelogram | |
---|---|

Using Base and Height | A = ½ × b × h |

Using Trigonometry | A = ab sin (x) |

Using Diagonals | A = ½ × d_{1} × d_{2} sin (y) |

Where,

- b = base of the parallelogram (AB)
- h = height of the parallelogram
- a = side of the parallelogram (AD)
- x = any angle between the sides of the parallelogram (∠DAB or ∠ADC)
- d
_{1}= diagonal of the parallelogram (p) - d
_{2}= diagonal of the parallelogram (q) - y = any angle between at the intersection point of the diagonals (∠DOA or ∠DOC)

**Note: **In the above figure,

- DC = AB = b
- AD = BC = a
- ∠DAB = ∠DCB
- ∠ADC = ∠ABC
- O is the intersecting point of the diagonals
- ∠DOA = ∠COB
- ∠DOC = ∠AOB

### Example Questions Using Parallelogram Area Formula

**Question 1:** Find the area of the parallelogram with the base of 4 cm and height of 5 cm?

**Solution:**

Given:

Base, b = 4 cm

h = 5 cm

We know that,

Area of Parallelogram = b×h Square units

= 4 × 5 = 20

Therefore, the area of a parallelogram = 20 cm^{2}

**Question 2:** Find the area of a parallelogram whose breadth is 8 cm and height is 11 cm?

**Solution:**

Given,

b = 8 cm

h = 11 cm

Area of a parallelogram

= b × h

= 8 × 11 cm^{2}

= 88 cm^{2}

**Question 3:** The base of the parallelogram is thrice its height. If the area is 192 cm^{2}, find the base and height.

**Solution:**

Let the height of the parallelogram = h cm

then, the base of the parallelogram = 3h cm

Area of the parallelogram = 192 cm^{2}

Area of parallelogram = base × height

Therefore, 192 = 3h × h

⇒ 3 × h^{2} = 192

⇒ h^{2} = 64

⇒ h = 8 cm

Hence the height of the parallelogram is 8 cm and breadth is

3 × h

= 3 × 8

= 24 cm

### More Topics Related to Parallelogram and Its Area

## Frequently Asked Questions

### What is a Parallelogram?

A parallelogram is a geometrical figure that has four sides formed by two pairs of parallel lines. In a parallelogram, the opposite sides are equal in length and opposite angles are equal in measure.

### What is the Area of a Parallelogram?

The area of any parallelogram can be calculated using the following formula:

Area = base Ã— height

It should be noted that the base and height of a parallelogram must be perpendicular.

### What is the Perimeter of a Parallelogram?

To find the perimeter of a parallelogram, add all the sides together. The following formula gives the perimeter of any parallelogram:

Perimeter = 2 (a + b)

### What is the Area of a Parallelogram Whose Height is 5 cm and Base is 4 cm?

The area of a perpendicular with height 5 cm and base 4 cm will be;

A = b Ã— h

Or, A = 4 Ã— 5 = 20 cm^{2}