The parallel sides of a Trapezium are 65 metres and 40 metres is non parallel sides are 39 and 56 metres find the area of the trapezium
Answers
Step-by-step explanation:
Draw the figure. If the height is h, then you have a 40-by-h rectangle in the center, with extra lengths of x and 25-x on the longer base.
x^2+h^2 = 56^2
(25-x)^2+h^2 = 39^2
x^2-56^2 = (25-x)^2 - 39^2
x = 224/5
so, h^2 = 56^2-x^2 = 28224/25
h = 168/5
so, the area is (40+65)/2 * 168/5 = 1764
Given : The parallel sides of a Trapezium are 65 metre and 40 metre
its non parallel sides are 39 and 56
To find : the area of the trapezium
Solution:
Ref attached figure :
DE and CF ⊥ AB
DE = CF = h cm
BF = x cm
=> AE = 65 + x - 40 - x = 25 + x cm
h² = 39² - x²
h² = 56² - (25 + x)²
=> 56² - (25 + x)² = 39² - x²
=> 3136 - 625 - x² - 50x = 1521 - x²
=> 50x = 990
=> x = 99/5
h² = 39² - x²
=> h² = 39² -(99/5)²
=> h² = 39² -(99/5)²
=> h = 168/5 cm
Area of trapezium = (1/2)(65 + 40) 168/5
= 1764 cm²
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