**Area of a
Trapezium**

**Area of a Trapezium Formula**

**Area of a Trapezium Formula**

**Area of the trapezium = ½ × ( a + b) × h**

**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**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:**