A plot is in the shape of a parallelogram.Two adjacent sides of this plot are 5m and 3.5m .One of its diagonal is 6.5m find the area of the plot
Answers
Given : A plot is in the shape of a parallelogram.Two adjacent sides of this plot are 5m and 3.5m .One of its diagonal is 6.5m
To find : the area of the plot
Solution:
Let say Height is h m
& base is 5 m
√(3.5² - h²) = x
6.5² = h² + (5 ± x)²
=> 6.5² - h² = ( 5 ± √(3.5² - h²))²
=> 6.5² - h² = 25 + 3.5² - h² ± 10√(3.5² - h²)
=> 5 = ±10√(3.5² - h²)
=> ±√(3.5² - h²) = 1/2
=> 3.5² - h² = 1/4
=> h² = 12
=> h = 2√3
Area of plot = base * height = 5 * 2√3
= 10√3 m²
= 17.32 m²
17.32 m² is the area of plot
Another way Apply hero formula
total area = 2 ( √s(s-a)(s-b)(s-c) ) as two triangle
a , , b , c are 5 , 3.5 , 6.5
s = 7.5
Area = 2 ( √7.5(2.5)(4)(1) ) = 10√3 m²
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