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Last modified on August 3rd, 2023

The area of a trapezoid is the total space enclosed by it. Since a trapezoid is a two-dimensional shape, its area also lies in a two-dimensional plane. The unit of area is in square units such as m^{2}, cm^{2}, in^{2} , or ft^{2}.

The basic formula to calculate the area of a trapezoid is given below:

Let us solve an example to understand the concept better.

**Find the area of a trapezoid whose base lengths are 14 cm and 9 cm, and height is 5 cm.**

Solution:

As we know,

Area (A) = ½ (a + b) × h, here a = 14 cm, b = 9 cm, and h = 5 cm

∴A = ½ (14 + 9) × 5

= 57.5 cm^{2}

We can calculate the area of a trapezoid when all 4 sides are known. There is no definite formula as such for such a circumstance. We try to calculate the area of the triangle as a portion formed in a trapezoid and then calculate the whole area of the trapezoid.

Let us solve an example to understand the concept better.

**Problem:** Finding the area of a trapezoid when the **SIDES** are known.

**Find the area of a non-isosceles trapezoid whose bases are 20 and 30, and the legs 12 and 16.**

Solution:

Let us label the trapezoid ABCD and mark the triangles Δ1 and Δ2, formed by 2 perpendiculars drawn in.

As we know,

Long base is 30 cm,

∴BE + FC = long base – short base

= 30 – 20

= 10 cm

Δ1 and Δ2 together forms a scalene triangle (3 unequal side lengths).

Here, we will use the **Heron’s Formula** to find the area of Δ1 and Δ2 together so as to find the perpendicular height of the trapezoid.

Area of Δ1 and Δ2 ** ${ =\sqrt{s\left( s-a\right) \left( s-b\right) \left( s-c\right) } }$** , here s = ½(a + b + c)

∴s = ½(a + b + c), here a = 10 cm, b = 12 cm, c = 16 cm

s = ½(10 + 12 + 16)

= 19 cm

Now, Area of Δ1 and Δ2 ${ =\sqrt{s\left( s-a\right) \left( s-b\right) \left( s-c\right) } }$ , here s = 19 cm

= √[19(19 – 10)(19 – 12)( 19 – 16)]

= 59.92 cm

Height (h) of a scalene triangle = 2A/b, here A = area, b = base

∴h = 2A/b, here A = 59.92 cm

∴h = 2 × 59.92/10

= 11.984 cm

Now, Area of trapezoid ABCD = ½ (a + b) × h, here a = 30 cm, b = 20 cm, h = 11.984 cm

∴A = ½ (30 + 20) × 11.984

= 299.6 cm

Last modified on August 3rd, 2023