Find the area of trapezium in which parallel sides are of length 5 cm and 11 cm whereas non parallel sides are of 4 cm and 6 cm.
Answers
Area of trapezium = 64√2 / 3 = 30.17 cm² in which parallel sides are of length 5 cm and 11 cm whereas non parallel sides are of 4 cm and 6 cm
Step-by-step explanation:
Lets draw perpendicular from vertex of 5 cm side at 11 cm side
Now let say distance left on 4 cm side = x cm
then Distance left on 6 cm side = 11 - 5 - x = 6 - x cm
now ⊥ height = h
h² = 4² - x²
h² = 6² - (6 - x)²
4² - x² = 6² - (6 - x)²
=> 16 - x² = 36 -(36 + x² - 12x)
=> 16 - x² = 12x - x²
=> 12x = 16
=> x = 16/12
=> x = 4/3
h² = 4² - x²
=> h² = 4² - (4/3)²
=>h² = 4²( 1 - 1/9)
=> h² = 4²(8/9)
=> h = 8√2 / 3
Area of trapezium = (1/2) (5 + 11)(8√2 / 3)
= 64√2 / 3
= 30.17 cm²
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