Area of a Trapezium
Area of a Trapezium Formula
How to Derive Area of a Trapezium Formula
In the given figure, ABCD is a
trapezium with AB || DC. Let us draw perpendiculars
DP and CQ on AB, from D and C,
respectively.
Let us consider DP = CQ = h,
i.e., the height of the trapezium ABCD.
From the given figure,
Area of the trapezium ABCD = Area of ΔDAP + Area of
rectangle DPQC + Area of ΔCQB
= ½ AP × h + PQ × h + ½ QB × h = ½ × h × (AP + 2PQ
+ QB)
= ½ × h × {(AP + PQ + QB) + PQ}
= ½ × h × (AB + PQ) [Since AP + PQ + QB =
AB]
= ½ × h × (AB + CD)
= ½ × h × (sum of the parallel
sides)
So, Area of the trapezium = ½ ×
altitude × sum of the parallel sides
= ½ × distance between the parallel
sides × sum of the parallel sides
Let the lengths of the parallel sides
be a and b.
Then, Area of the trapezium = ½ × (a + b) × h
How To Calculate Area of Trapezium?
Follow the below steps to find the area of a trapezium:
- Step 1: Find and note down the lengths of the parallel sides (bases) of the trapezium from the given data.
- Step 2: Calculate the sum of the lengths of the parallel sides.
- Step 3: Multiply the value of the sum of parallel sides by height of the trapezium and again by 1/2.
- Step 4: Write the answer in square units. This is the required area of the trapezium.
Area of Trapezium Examples
Example 1: The parallel sides of a trapezium are 25 cm and 15 cm long. If the distance between them is 12 cm, find the area of the trapezium.
Solution:
Here, a = 25 cm and b = 15 cm
Distance between the parallel sides
(h) = 12 cm
Area of the trapezium = ½ × (a + b) ×
h
= ½ ×
(25 + 15) × 12
= ½ ×
40 × 12 = 240 sq. cm
Example 2:
Find the distance between the parallel sides of a trapezium whose parallel
sides are 16 cm and 14 cm and the area of the trapezium is 270 sq. cm.
Solution:
Here, a = 16 cm and b = 14 cm
Given: Area of the trapezium = 270 sq.
cm
Distance between the parallel sides
(h) = ?
Area of the trapezium = ½ × (a + b) ×
h
270 = ½ × (16 +
14) × h
270 = ½ × 30 × h
270 = 15 × h
h = 270/15
h = 18 cm
Example 3:
Find the area of a trapezium whose parallel sides are 18 cm and 16 cm,
respectively, and the distance between them is 10 cm.
Solution:
Here, a = 18 cm and b = 16 cm
Distance between the parallel sides
(h) = 10 cm
Area of the trapezium = ½ × (a + b) ×
h
= ½ × (18
+ 16) × 10
= ½ × 34
× 10 = 170 sq. cm
Example 4: Find the height of a trapezium whose parallel sides are 24 cm and 20 cm, respectively, and the area of the trapezium is 330 sq. cm.
Solution:
Here, a = 24 cm and b = 20 cm
Given: Area of the trapezium = 330 sq.
cm
Distance between the parallel sides
(h) = ?
Area of the trapezium = ½ × (a + b) ×
h
330 = ½ × (24 +
20) × h
330 = ½ × 44 ×
h
330 = 22 × h
h = 330/22
h = 15 cm
To find the area of a rhombus and the area of a parallelogram, click the following links: