Area of Plane Shapes
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
www.almerja.com
الجزء والصفحة:
...
14-3-2017
1369
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Triangle
Area = ½ × b × h
b = base
h = vertical height
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Square
Area = a2
a = length of side
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Rectangle
Area = w × h
w = width
h = height
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Parallelogram
Area = b × h
b = base
h = vertical height
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Trapezoid (US)
Trapezium (UK)
Area = ½(a+b) × h
h = vertical height
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Circle
Area = π × r2
Circumference = 2 × π × r
r = radius
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Ellipse
Area = πab
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Sector
Area = ½ × r2 × θ
r = radius
θ = angle in radians
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Note: h is at right angles to b:
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Example: What is the area of this rectangle?
The formula is:
Area = w × h
w = width
h = height
We know w = 5 and h = 3, so:
Area = 5 × 3 = 15
Example: What is the area of this circle?
Radius = r = 3
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Area
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= π × r2
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= π × 32
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= π × (3 × 3)
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= 3.14159... × 9
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= 28.27 (to 2 decimal places)
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Example: What is the area of this triangle?
Height = h = 12
Base = b = 20
Area = ½ × b × h = ½ × 20 × 12 = 120
A harder example:
Example: Sam cuts grass at $0.10 per square meter
How much does Sam earn cutting this area:
Let's break the area into two parts:
Part A is a square:
Area of A = a2 = 20m × 20m = 400m2
Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.
Area of B = ½b × h = ½ × 20m × 14m = 140m2
So the total area is:
Area = Area of A + Area of B = 400m2 + 140m2 = 540m2
Sam earns $0.10 per square meter
Sam earns = $0.10 × 540m2 = $54
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