Mathematics Coursework - Fencing
Introduction:
A framer has a farm that he needs to fence, and I need to investigate and look for the largest area of a plot with the perimeter of 1000 meter.
I will start from triangle the least sided shape.
(All diagram not drawn to scale)
Triangles:
Equilateral Triangle:
A triangle that has the same length on every side is known as an equilateral triangle.
Formula: (Base x Height) ?2
Equilateral Triangle 1:
Height:
H2+ 166.72 = 333.32 (Pythagoras Theorem)
H2 = 111088.89 - 27788.89
H2 = 83300
H = 288.6m (1 d.p.)
Area of triangle:
(288.62 x 166.7) m
= 48112.5m2 (1 d.p.)
Isosceles Triangles:
Isosceles triangle means a triangle that has two same lengths on the side and the bottom two angles will be the same.
Formula: (Base x Height) ?2
Isosceles Triangle 1:
Sides 262.5
Base 475
Perimeter:
(2 x 262.5 + 475) m
= 1000m
Height:
H2 + 237.52 = 262.52
H2 = 68906.25 - 56406.25
H2 = 12500
H = 111.8m (1 d.p.)
Area of triangle:
(111.8 x 237.5) m
= 26553.3m (1 d.p.)
Isosceles Triangle 2:
Sides 317
Base 366
Perimeter:
(2 x 317 + 366) m
= 1000m
Height:
H2 + 1832 = 3172
H2 = 100489 - 33489
H2 = 67000
H = 258.84m (2 d.p.)
Area of triangle:
(258.84 x 183) m
= 47368.38 m2 (2 d.p.)
Right angle triangles:
A triangle that has a right angle is called a right angle triangle.
Formula: (Base x Height) ?2
Right angle triangle 1:
Hypotenuse:
22 + 42 = AB2
4 + 16 = AB2
20 = AB2
AB = 4.47m (2 d.p.)
Perimeter:
(2 + 4 + 4.47) m
= 10.47m
Ratio:
If 10.47 = 1000 2=X 4=Y 4.47=Z
000 ? 10.47
= 95.5
Length:
2=X X = 2x 95.5
X = 191 m
4=Y
Y = 4 X 95.5
Y = 382 m
Area:
(191 x 382 ? 2) m
= (72962 ? 2)
= 36481 m2
Right angle triangle 2:
Hypotenuse:
82 + 112 = AB2
64 + 121 = AB2
185 = AB2
AB = 13.6m (1 d.p.)
Perimeter:
(8 + 11 + 13.6) m
= 32.6m
Ratio:
If 32.6 = 1000 8=X 11=Y 13.6=Z
000 ? 32.6
= 30.67 (2 d.p.)
Length:
8=X X = 8 x 30.67
X = 245.4 m (1 d.p.)
1=Y
Y = 11 X 30.67
Y = 337.4 m (1 d.p.)
Area:
(245.4 x 337.4 ? 2) m
= (82797.96 ? 2) m
= 41398.98 m2
Scalene triangles:
Scalene triangle is a triangle that has any value of sides.
Scalene triangle 1:
Formula:
? s (s-a)(s-b)(s-c)
s = half perimeter
a, b, c = sides
Introduction:
A framer has a farm that he needs to fence, and I need to investigate and look for the largest area of a plot with the perimeter of 1000 meter.
I will start from triangle the least sided shape.
(All diagram not drawn to scale)
Triangles:
Equilateral Triangle:
A triangle that has the same length on every side is known as an equilateral triangle.
Formula: (Base x Height) ?2
Equilateral Triangle 1:
Height:
H2+ 166.72 = 333.32 (Pythagoras Theorem)
H2 = 111088.89 - 27788.89
H2 = 83300
H = 288.6m (1 d.p.)
Area of triangle:
(288.62 x 166.7) m
= 48112.5m2 (1 d.p.)
Isosceles Triangles:
Isosceles triangle means a triangle that has two same lengths on the side and the bottom two angles will be the same.
Formula: (Base x Height) ?2
Isosceles Triangle 1:
Sides 262.5
Base 475
Perimeter:
(2 x 262.5 + 475) m
= 1000m
Height:
H2 + 237.52 = 262.52
H2 = 68906.25 - 56406.25
H2 = 12500
H = 111.8m (1 d.p.)
Area of triangle:
(111.8 x 237.5) m
= 26553.3m (1 d.p.)
Isosceles Triangle 2:
Sides 317
Base 366
Perimeter:
(2 x 317 + 366) m
= 1000m
Height:
H2 + 1832 = 3172
H2 = 100489 - 33489
H2 = 67000
H = 258.84m (2 d.p.)
Area of triangle:
(258.84 x 183) m
= 47368.38 m2 (2 d.p.)
Right angle triangles:
A triangle that has a right angle is called a right angle triangle.
Formula: (Base x Height) ?2
Right angle triangle 1:
Hypotenuse:
22 + 42 = AB2
4 + 16 = AB2
20 = AB2
AB = 4.47m (2 d.p.)
Perimeter:
(2 + 4 + 4.47) m
= 10.47m
Ratio:
If 10.47 = 1000 2=X 4=Y 4.47=Z
000 ? 10.47
= 95.5
Length:
2=X X = 2x 95.5
X = 191 m
4=Y
Y = 4 X 95.5
Y = 382 m
Area:
(191 x 382 ? 2) m
= (72962 ? 2)
= 36481 m2
Right angle triangle 2:
Hypotenuse:
82 + 112 = AB2
64 + 121 = AB2
185 = AB2
AB = 13.6m (1 d.p.)
Perimeter:
(8 + 11 + 13.6) m
= 32.6m
Ratio:
If 32.6 = 1000 8=X 11=Y 13.6=Z
000 ? 32.6
= 30.67 (2 d.p.)
Length:
8=X X = 8 x 30.67
X = 245.4 m (1 d.p.)
1=Y
Y = 11 X 30.67
Y = 337.4 m (1 d.p.)
Area:
(245.4 x 337.4 ? 2) m
= (82797.96 ? 2) m
= 41398.98 m2
Scalene triangles:
Scalene triangle is a triangle that has any value of sides.
Scalene triangle 1:
Formula:
? s (s-a)(s-b)(s-c)
s = half perimeter
a, b, c = sides
