Field book of an agricultural land is given in the figure. It is divided into 4 plots . Plot I is a right triangle , plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)
Answers
Given : agricultural land is divided into 4 plots . Plot I is a right triangle , plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium,
To find : area of each plot and the total area of the field
Solution:
AC = 13 cm
AD = 19 - 7 = 12 cm
CD² = AC² - AD² = 13² - 12²
=> CD² = 25
=> CD = 5 cm
area Plot I = (1/2) * 5 * 12 = 30 cm²
area plot II = (√3 / 4) 13² = 73.1 cm²
area plot III = 7 * 5 =35 cm²
Let say height of trapezium = h
=> √9² - h² + 5 + √15² - h² = 17
=> √9² - h² + √15² - h² = 12
=> √15² - h² = 12 - √9² - h²
=> 15² - h² = 144 + 9² - h² - 24√9² - h²
=> √9² - h² = 0
=> h = 9 => FG ⊥ GH
area plot IV = (1/2) (17 + 5) * 9 = 99 cm²
Total Area = 30 + 73.1 + 35 + 99 = 237.1 cm²
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