Table of Contents
The area of the quadrilateral refers to the region that is present inside it. The area of the Quadrilateral is enclosed by its 4 sides. A Quadrilateral is a four-sided paragon. In the Quadrilateral there are four vertices, four angles, four diagonals, and four sides. There are six types of Quadrilateral. The examples of quadrilaterals are square, rectangle, parallelogram, rhombuses, kite, and trapezoid.
In this article, we will discuss the Area of Quadrilateral, their types, formulas, properties of quadrilaterals, etc.
Also Check: Average
What is the Area of the Quadrilateral?
The Area of a Quadrilateral is a region enclosed by all the sides of the Quadrilateral. It is defined as the region occupied by the boundary of a flat object. The measurement is done In square units with square metres ( m²). The method of the Area of Quadrilateral depends on the type of quadrilateral.
Types of Quadrilateral
There are major two types of Quadrilateral.
- Regular Quadrilateral
- Irregular Quadrilateral
Definition of Regular Quadrilateral
A regular Quadrilateral is a four-sided shape where all sides and angles are equal in length.
Definition of Irregular Quadrilateral
An irregular Quadrilateral is a four-sided shape where all sides and angles are not all equal.
Also Check: Circumstance of Circle
Area of Quadrilateral formula
Formulas of the area of Quadrilateral for various types of Quadrilateral are given below:
| Quadrilateral Names | Area |
| Rhombus | 12 d1 d2 , where d1 and d2 are the diagonals of the rhombus. |
| Parallelogram | b h, where b is the breadth while h is the height. |
| Square | a2, where a is the side of the square. |
| Rectangle | l b where l is the length and b is the breadth of the rectangle. |
| Kite | 12 d1 d2 , where d1 and d2 are the diagonals of the rhombus. |
| Trapezoid | 12 (a + b) h |
Also Check: Algebraic Expressions
Area of Quadrilateral
The area of the Quadrilateral formula Dividing into two triangles :
The BD length in Quadrilateral ABCD is d. The diagonal BD can divide ABCD into triangles BAD and BCD. We determine the area of each triangle to add up the area of the Quadrilateral ABCD.
Triangle ABD Area = ½ ×d × h1
Triangle BCD Area = ½ ×d × h2
The area of the quadrilateral ABCD = area of triangle ABD + area of triangle BCD.
Thus the area of Quadrilateral ABCD = ½ ×d × h1 + ½ ×d × h2 = ½ ×d × (h1 + h2)
Thus, using this formula we can find the area of the Quadrilateral.
Area of Quadrilateral using Heron’s formula
Heron’s formula is used to find the area of a triangle if the three sides of the triangle are given. Follow these steps to find the Area of the Quadrilateral given below:
Step 1: Divide the Quadrilateral into two triangles. Using a diagonal whose diagonal length is known.
Step 2: Apply Heron’s formula to find the area of the Quadrilateral.
Heron’s Formula = Area (A) = s (s – a)(s – b)(s – c) , where is the perimeter while a, b, and c are the sides of the triangle.
Step 3: Now add the area of two triangles to find the area of the Quadrilateral.
Area Formula of Different Types of Quadrilaterals
There are 6 types of Quadrilateral. These are square, rectangle, parallelogram, rhombuses, kite, trapezoid. There are specific formulas to find the area of each of these Quadrilaterals. These formulas are given below:
Area of square
The Quadrilateral which has four equal sides and four equal lengths is known as square. It is also a regular Quadrilateral its equal sides and equal angles.
The formula of the area of the square = a × a = a² square unit
Where “a” is the length of the Sides of Square.
Area of parallelogram
A parallelogram is a simple Quadrilateral. Parallelogram Quadrilateral has opposite sides that are equal. It also has equal to opposite angles.
The formula of the area of the parallelogram = b × h square unit
where “b” is the base length and “h” is the height of the parallelogram.
Area of rectangle
A rectangle Quadrilateral has four right angles. Every angle in a rectangle is 90°. A rectangle has parallel sides as well as equal opposite sides. It’s diagonal cut in half.
The formula of the area of the rectangle = l ×b square unit
where “l” is the length and “height” of the parallelogram.
Area of rhombus
In a rhombus Quadrilateral its opposite sides are parallel to one another. Its four sides are the same length. However, the angles are equal to 90° (degree).
The formula of the area of the rhombus = (½)×d¹×d² square unit
There “d¹” and “d²” are the two diagonals of rhombus.
Area of kite
In kite Quadrilateral, it has two pairs of sides. These sides are equal in length. The diagonals are equal to 90°.
The formula of the area of the kite = (½)pq square unit
where “p” and “q” are two diagonals of the kite.
Area of trapezoid
Trapezoid Quadrilateral is a combination of two triangles. It has two parallel sides.
The formula of the area of the trapezoid = (½)(a+b) h square unit
where “a” and “b” are the lengths of parallel sides and “h” is the height of the trapezoid.
Perimeter of Quadrilateral
A Quadrilateral is a four-sided polygon. It can be regular or Irregular. The perimeter of a Quadrilateral is the total length of its boundary.
- In the regular perimeter Quadrilateral, its sides and angles are equal in length and measure.
- In the Irregular perimeter Quadrilateral, its sides and angles are not equal.
Perimeter of Quadrilateral formula
By adding all its side lengths we can obtain the perimeter of the Quadrilateral. The formula for the perimeter of the Quadrilateral is:
Perimeter = a + b + c + d
Where, a, b, c, and d are the sides of the given quadrilateral figure.
Properties of Quadrilateral
- Every Quadrilateral encloses four vertices and four sides as well as four angles.
- The sum of its angles is 360°(degree).
- Generally, a Quadrilateral has different lengths and angles of different measures.
- Quadrilaterals are in 2D shapes.
Area of Quadrilateral: Solved Examples
Q.1. Find the area of a rectangle with a length of 8 cm and a width of 5 cm.
Ans. We know that the formula of the area of the rectangle = l ×b square unit
Therefore, The area of the rectangle = 8 × 5 square unit
= 40 cm square
2. Find the area of a parallelogram with a base of 12 m and a height of 7 m.
Ans. We know that the formula of the area of the parallelogram = b × h square unit
Therefore, the area of the parallelogram = b × h square unit
= 12 7 = 84 m square.
3. Find the area of a trapezoid with bases of 10 cm and 6 cm and a height of 4 cm.
Ans. we know that The formula of the area of the trapezoid = (½)(a+b) h square unit
Therefore, the area of the trapezoid = (½)(10+6) 4 square unit
= (½)(16) 4 square unit
= (16) 2 = 32 square unit
Area of Quadrilateral: Practice Questions
- Find the area of a rectangular tray with a length of 18 cm and a width of 9 cm.
- Find the area of a parallelogram with a base of 22 m and a height of 8 m.
- Find the area of a trapezoid with bases of 12 cm and 8 cm and a height of 2 cm.
FAQs: Area of Quadrilaterals
Can side lengths alone determine the area?
Sides cannot always alone determine the area of the given quadrilateral. For some quadrilaterals, we need more information like angles or diagonals.
What is the formula for the area of a rectangle?
Area of a rectangle = Length × Width.
How do you find the area of a parallelogram?
Area of a parallelogram = Base × Height.
How to calculate the area of a trapezoid?
Area of a trapezoid = ½ × (Base₁ + Base₂) × Height.
