Area of a Trapezoid the area enclosed by the 2-D figure Trapezoid. It is the total space occupied by the boundary of the trapezoid. A trapezoid is another name for a trapezium and the area of a trapezoid is easily found if the parallel side and the height of the trapezoid are given. It is calculated in square units, i.e. cm2, m2, in2, etc.
In this article, we have added, Trapezoid Definition, Area of Trapezoid, Trapezoid Formula, and others in detail.
What is a Trapezoid?
A trapezoid is a polygon with just one pair of parallel sides. These parallel sides are called the bases of the Trapezoid. The other two sides of trapezoids are non-parallel and are referred to as the Legs of the Trapezoid. The image added below shows a trapezoid with its base and legs.
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What is Area of Trapezoid?
Area of the trapezoid is the space occupied by the perimeter of the trapezoid. It is the 2-D space occupied by the boundaries of the trapezium. It is the half of the product of sum of parallel side with its sides. It is calculated in square units similar to other areas.
In a trapezoid, we have a pair of parallel lines and the area of a trapezoid is found by multiplying the sum of the parallel side of a trapezoid with the height of the trapezoid and then dividing the whole product by 2.
Formula that is used to calculate the area of trapezoid is added below:
To calculate the area of a trapezoid, we must know the lengths of two of parallel sides and the distance (height) between them. The area (A) of a trapezoid is given by the formula,
A = ½ (a + b) h
where,
- a and b are the Parallel Bases of Trapezoid
- h is the Height of Trapezoid
How to Calculate Area of Trapezoid
Area of trapezoid can be found using the following sequence of steps:
Step 1: Calculate the lengths of the parallel sides (bases) of trapezoid.
Step 2: Sum of the bases of the trapezoid is calculated.
Step 3: Value of the sum of bases is multiplied by the height or altitude of the trapezoid and then by 1/2.
Step 4: Answer is then further simplified and is written in terms of square units.
To derive area of trapezoid we divide the trapezoid into a triangle by dividing one leg of the trapezoid into two equal halves and the joining the mid point of the leg to the opposite vertex.
Then we take this triangle so form and then arrange it such that it forms a bigger triangle. The image added below shows how the trapezoid is converted into a triangle.
Now,
Area of Trapezoid (A) = Area of Triangle
A = ½ × base × height
A = ½ (a + b) h
Thus, the formula for area of trapezoid is derived.
Area of Trapezoid without Height
To find the area of the trapezoid (Isosceles Trapezoid) if the height of trapezoid is not given and all its sides are given we follow the steps added below. Area of trapezoid is not calculated without using the height of the trapezoid so we first find the height of the trapezoid with the given information and then easily find the area of the trapezoid, using area of trapezoid formula.
Suppose we are given a trapezoid, ABCD with sides AB and CD are parallel and AD and BC are equal sides. The image showing the trapezoid ABCD is added below,
Now we draw two perpendiculars from vertex A and vertex B to side CD and name then AP and AQ respectively. Thus, the height of the trapezoid is AP = AQ = (h). Now height of the trapezoid is easily found using the Pythagoras Theorem if all the sides of the trapezoid are given.
After finding the height of the trapezoid we can easily found the area of the trapezoid.
Perimeter of Trapezoid
Perimeter of trapezoid is defined as the sum of all the sides of the trapezoid. The formula for the perimeter of a trapezoid when the sides are “a”, “b”, “c”, and “d” is given by,
Perimeter (P) = (a + b + c + d) units
Area of Trapezoid Examples
Example 1: Find the area of a trapezoid for base lengths 10 units and 15 units and height of 8 units.
Solution:
Given,
Area of Trapezoid Formula is,
A = 1/2 (a + b) h
A = 1/2 (10 + 15) 8
A = 100 sq. units
Example 2: If the area of a trapezoid is 120 square units and length of its parallel side are 12 unit and 8 unit, then find the height of the trapezoid.
Solution:
Given,
- a = 12 units
- b = 8 units
- A = 120 square units
Area of Trapezium(A) = 1/2(a + b)h
120 = 1/2(12 + 8)h
240 = 20.h
h = 240/20 = 12 units.
Thus, the height of trapezoid is 12 units.
Example 3: Find the area of a trapezoid for base lengths 12 units and 18 units and height of 16 units.
Solution:
Given,
Area of Trapezoid Formula is,
A = 1/2 (a + b) h
A = 1/2 (12 + 18) 16
A = 240 sq. units
Example 4: If the area of a trapezoid is 200 square units and length of one of its parallel side is 15 units and its height is 20 units, then find the length of other parallel side of the trapezoid.
Solution:
Given,
- a = 15 units
- h = 20 units
- A = 200 square units
Area of Trapezium(A) = 1/2(a + b)h
200 = 1/2(15 + b)20
400/20 = 15 + b
b = 20 – 15 = 5 units
Thus, the length of parallel side of the trapezoid is 5 units.
Q1. Find the height of a trapezoid with base lengths 10 units and 15 units and area 125 square units.
Q2. Find the area of a trapezoid for base lengths 12 units and 18 units and height of 16 units.
Q3. Find the area of a trapezoid for base lengths 4 units and 6 units and height is equal to the side of square whose are is 121 sq. units.
Q4. Find the area of a trapezoid if its height is 10 units and bases are equal to the side of the rectangle whose area is 120 sq units and perimeter is 48 units.
Area of Trapezoid – FAQs
What is Area of Trapezoid in Maths?
Area of Trapezoid in Mathematics is defined the area occupied by boundaries of trapezoid in 2-D space. It is measure in (unit)2.
What is the Formula for the Area of a Trapezoid?
Area of Trapezoid is calculated using the formula,
Area of Trapezoid = (a + b)/2.h
How do you find the Area of a Trapezium with 4 Sides?
Area of Trapezium with four sides can easily be calculated when four sides are given using the Pythagoras theorem to find the height of the trapezoid and then we find the area of trapezoid using the area of trapezoid formula.
What is Area of a 4 Sided Figure?
Area of a four sided figure is calculated using the formula,
Area of 4 Sided Figure = Base × Height
What is a Trapezoid?
Trapezoid is a type of quadrilateral, i.e. a polygon with four side. It is other name of trapezium and it has a pair of parallel sides.
What is Perimeter of Trapezoid?
Perimeter of Trapezoid is sum of all boundaries of trapezoid. Suppose if we have a trapezoid with sides, a, b, c and d then its perimeter is given using the formula,
Perimeter of Trapezoid = (a + b + c + d) units
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