Question

the parallel sides of a trapezium are 20cm and 10 cm it's nonparallel sides are both equal each being 13 cm find the area of the trapezium​

Answer 1

Step-by-step explanation:

use this formula and ver answer

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• The parallel sides of a trapezium = 20 cm & 10 cm
• Non - parallel sides = 13 cm

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of trapezium according to the given question.

We have,

• AB = 10 cm
• CD = 20 cm
• AD = 13 cm

→ 2DE = EF

→ DE = 10/2

→ DE = 5 cm

$\underline{\underline{\tt{By\:\:Pythagoras\:\:theorem\::}}}$

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (AD)² = (DE)² + (AE)²

⇒ (13)² = (5)² + (AE)²

⇒ (AE)² = 13² - 5²

⇒ (AE)² = 169 - 25

⇒ (AE)² = 144

⇒ AE = √144

⇒ AE = 12 cm

Now,

As we know that formula of the area of trapezium;

$\boxed{\bf{Area = \frac{1}{2} \times (sum\:of\:base) \times height }}$

A/q

$\mapsto\tt{Area = \dfrac{1}{2} \times (10 + 20) \times 12}$

$\mapsto\tt{Area = \dfrac{1}{2} \times (30) \times 12}$

$\mapsto\tt{Area = \dfrac{1}{\cancel{2}} \times (30) \times \cancel{12}}$

$\mapsto\tt{Area = (30 \times 6)}$

$\mapsto\bf{Area = 180\:cm^{2}}$

Thus,

The area of the trapezium will be 180 cm² .