Answer:
Total area = 237.09 cm²
Step-by-step explanation:
Given question is incomplete; here is the complete question.
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)
From the figure attached,
Area of the right triangle I = [tex]\frac{1}{2}(\text{Base})\times (\text{Height})[/tex]
Area of ΔADC = [tex]\frac{1}{2}(\text{CD})(\text{AD})[/tex]
= [tex]\frac{1}{2}(\sqrt{(AC)^2-(AD)^2})(\text{AD})[/tex]
= [tex]\frac{1}{2}(\sqrt{(13)^2-(19-7)^2} )(19-7)[/tex]
= [tex]\frac{1}{2}(\sqrt{169-144})(12)[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Area of equilateral triangle II = [tex]\frac{\sqrt{3} }{4}(\text{Side})^2[/tex]
Area of equilateral triangle II = [tex]\frac{\sqrt{3}}{4}(13)^2[/tex]
= [tex]\frac{(1.73)(169)}{4}[/tex]
= 73.0925
≈ 73.09 cm²
Area of rectangle III = Length × width
= CF × CD
= 7 × 5
= 35 cm²
Area of trapezium EFGH = [tex]\frac{1}{2}(\text{EF}+\text{GH})(\text{FJ})[/tex]
Since, GH = GJ + JK + KH
17 = [tex]\sqrt{9^{2}-x^{2}}+5+\sqrt{(15)^2-x^{2}}[/tex]
12 = [tex]\sqrt{81-x^2}+\sqrt{225-x^2}[/tex]
144 = (81 - x²) + (225 - x²) + 2[tex]\sqrt{(81-x^2)(225-x^2)}[/tex]
144 - 306 = -2x² + [tex]2\sqrt{(81-x^2)(225-x^2)}[/tex]
-81 = -x² + [tex]\sqrt{(81-x^2)(225-x^2)}[/tex]
(x² - 81)² = (81 - x²)(225 - x²)
x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴
144x² - 11664 = 0
x² = 81
x = 9 cm
Now area of plot IV = [tex]\frac{1}{2}(5+17)(9)[/tex]
= 99 cm²
Total Area of the land = 30 + 73.09 + 35 + 99
= 237.09 cm²
