field book of agricultural land .it is divided into 4 plots. plot 1 is a right angle triangle , plot 2 is an equilateral triangle, plot 3 is a rectangle, plot 4 is a trapezium . find the area of each plot and total the area of field(use√3=1.73)

Plot 1 area= 32.5cm²

Plot 2 area = 73.0925cm²

Plot 3 area = 35cm²

Plot 4 area = 54cm²

Total the area of field = 194.5925cm²

Step-by-step explanation:

To find the area of each plot, we need to find the area of the shape of each plot.

A diagram related to the question found at (question ID: 18861101)

has been attached.

Plot 1 is a right angle triangle:

Area = ½ × base × height

AE = 19cm, CF = DE = 7cm

Ad = AE - DE

base =AD =  19-7 = 12cm

Using Pythagoras theorem

height = CD = √(AC² - AD)²

AC = 13cm

CD = √(13² - 12²) = √(169-144)

height = CD = √25 = 5

Area = ½ × 13×5 = 65/2

Area = 32.5cm²

Plot 2 is an equilateral triangle

Area = ½ × base × height

Area of the equilateral triangle = s²/4 ×(√3)

Where s = side = 13cm

√3=1.73

Area of the equilateral triangle = (13)²/4 ×(√3) = 169/4 × 1.73

= 42.25 × 1.73 = 73.0925cm²

Plot 3 is a rectangle

Area of the rectangle = length × width

length = FC = 7cm

width = CD = 5cm

Area of the rectangle = 7×5 = 35cm²

Plot 4 is a trapezium

Area of trapezium = ½(a+b) × height

a = FE = CD = 5cm

b = GH = 17cm

Height = ?

To get night let's break the trapezium diagram. We would have two triangles and 1 rectangle.

FE = CD= 5cm

From the 2nd diagram of the triangle,

Using Pythagoras theorem to find h in  both triangles:

9² = h²+x²

h² = 81-x² ...(1)

15² = h²+(12-x)²

225 = h² +144-24x+x²

81 = h²-24x+x² ...(2)

Substitute 1 in 2

81 = 81-x² + x²-24x

24x = 0

x = 0

h² = 81-0² = 81

h = √81 = 9cm

base of the triangle = GH-FE = 17-5 = 12cm

Area of trapezium = ½(5+7) × 9

= 12/2 × 9 = 54cm²

Total the area of field = area of right angled triangle + area of equilateral triangle + area of rectangle +area of trapezium

= 32.5cm² + 73.0925cm² + 35cm² + 54cm²

Total the area of field = 194.5925cm²

step-by-step explanation: