the shape of a piece of land is a parallelogram whose adjacent sides are 12metre and 9 metre and the corresponding diagonal is 15 metre find the area of the land
Answers
The area of the land (A₁) is 108 m².
Given:
The sides of a parallelogram are 12 meters and 9 meters and the corresponding diagonal is 15 meters.
To Find:
The area of land is in a parallelogram shape.
Solution:
We are required to find the area of the land.
Area of parallelogram = 2×Area of the triangle (adjacent sides and a diagonal)
The area of a triangle is given as
Area of triangle, A = √s(s−a)(s−b)(s−c) ---------(1)
Where a, b, and c are the sides of the triangle
Where a = 12 m, b = 9 m, c = 15 m
Semi perimeter, s = (a+b+c)/2 -------(2)
Substitute values of a, b, and c in equation(2)
s = (12+9+15)/2
s = 36/2
s = 18
On substituting the values of a, b, c, and s in equation(1) we get
A = √18(18-12)(18-9)(18-15)
A = √18×6×9×3
A = √2916
A = 54 m²
We know the area of the land in rhombus shape, A₁ = 2×Area of a triangle(A)
A₁ = 2×54
A₁ = 108 m²
Therefore, The area of the land (A₁) is 108 m².
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