Question

two parallel sides DC and ab of a Trapezium are 12 cm and 36 CM respectively if non parallel sides are each equal to 15 cm find the area of trapezium ​

Answer 1

Refer the attachment for figure.

Given :

Ab = 36 cm and CD = 12 cm and non parallel sides i.e. AD = CB = 15 cm.

Find :

Area of trapezium.

Solution :

→ AB = 36 cm

→ CD = EF = 12 cm

So,

→ AE = (AB - EF)/2

→ AE = (36 - 12)/2

→ AE = 24/2

→ AE = 12 cm

Now,

In $\triangle{ADE}$

By Pythagoras Theorem

→ (AD)² = (AE)² + (DE)²

→ (15)² = (12)² + (DE)²

→ 225 = 144 + (DE)²

→ 225 - 144 = (DE)²

→ 81 = (DE)²

→ DE = 9 cm

(height of trapezium)

We know that

Area of trapezium = 1/2 × h(a + b)

Here,

• h = 9 cm
• a = 36 cm
• b = 12 cm

Put them in above formula

→ 1/2 × 9 (36 + 12)

→ 9/2 (48)

→ 9(24)

→ 216 cm²

∴ Area of trapezium is 216 cm².

Answer 2

Answer:

Step-by-step explanation:

Given :

Ab = 36 cm and CD = 12 cm and non parallel sides i.e. AD = CB = 15 cm.

Find :

Area of trapezium.

Solution :

→ AB = 36 cm

→ CD = EF = 12 cm

So,

→ AE = (AB - EF)/2

→ AE = (36 - 12)/2

→ AE = 24/2

→ AE = 12 cm

Now,

In  

By Pythagoras Theorem

→ (AD)² = (AE)² + (DE)²

→ (15)² = (12)² + (DE)²

→ 225 = 144 + (DE)²

→ 225 - 144 = (DE)²

→ 81 = (DE)²

→ DE = 9 cm

(height of trapezium)

We know that

Area of trapezium = 1/2 × h(a + b)

Here,

h = 9 cm

a = 36 cm

b = 12 cm

Put them in above formula

→ 1/2 × 9 (36 + 12)

→ 9/2 (48)

→ 9(24)

→ 216 cm²

∴ Area of trapezium is 216 cm².