Question

The parallel sides of a Trapezium are 52 cm and 27 cm, and the other two sides are 25 cm and 30 cm .find the area of trapezium. by Pythagoras Theorem method

please solve this problem

Answer 1

Answer:

948 cm²

Step-by-step explanation:

Given, parallel sides are 52 cm and 27 cm.

Given, non-parallel sides are 25 cm and 30 cm.

(i)

Let the height be 'h' cm.

By Pythagoras theorem, we get

⇒ √30 - h² + √25 - h² = 52 - 27

⇒ √30 - h² + √25 - h² = 25

⇒ (√30 - h²) = (25 - √25 - h²)

On squaring both sides, we get

⇒ (√30 - h²)² = (25 - √25 - h²)²

We know that (a - b)² = a² + b² - 2ab

⇒ 900 - h² = (625) - (2 * 25 * √25-h²) + (√25 - h²)²

⇒ 900 - h² = 625 - (50 * √25-h²) + (25² - h²)

⇒ 900 - h² = 625 - 50√25-h² + 625 - h²

⇒ 900 = 1250 - 50√25-h²

⇒ -350 = -50√25-h²

On squaring both sides, we get

⇒ (-350)² = (-50√25-h²)²

⇒ 122500 = 2500(25² - h²)

⇒ 122500 = 1562500 - 2500h²

⇒ 576 = h²

⇒ h = 24 cm.

Hence, height of trapezium = 24 cm.

(ii)

We know that Area of trapezium = (1/2) * (Sum of parallel sides) * height

⇒ (1/2) * (52 + 27) * 24

⇒ (1/2) * (79) * 24

⇒ 948 cm²

Therefore, Area of trapezium = 948 cm².

Hope it helps!