Answer:
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 brainly (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
