Area And Perimeter ALPHA Maths Module : Pipeng Free Online Software

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Pipeng Free Online Software : Area And Perimeter ALPHA Maths Module

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Pipeng : Maths Geometry : Area And Perimeter Or Circumference ALPHA Maths Homework Module

Area And Perimeter ALPHA Maths Module

Description : Maths Geometry : Area And Perimeter Or Circumference

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ALPHA : Geometry : Circle 01 : Area And Perimeter Of A Circle : ALPHA Maths Homework Exercise

Description : Area and perimeter of a circle.

Discussion : A circle has constant radius or diameter. The diameter is twice the radius. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 4 questions.

area A

perimeter p

radius r from A

diameter d from p

The equations are :

A = π r² = π d² / 4

p = 2 π r = π d

r = √(A / π)

d = p / π

where

d = diameter

r = radius = d / 2

A = area

p = perimeter or circumference

ALPHA : Geometry : Circle 02 : Area Of An Ellipse : ALPHA Maths Homework Exercise

Description : Area of an ellipse.

Discussion : An elipse is formed by cutting across a cone at an angle. An elipse has two diameters or axis, the major axis (the larger axis), and the minor axis (the smaller axis). The perimeter or circumference of an ellipse is calculated using elliptic integrals and is not included in this homework exercise. The axis used are the half axis, corresponding to radius. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 3 questions.

area A

major axis a

minor axis b

The equations are :

A = π a b

a = A / (π b)

b = A / (π a)

where

a b = major and minor half axis

A = area

ALPHA : Geometry : Circle 03 : Area And Perimeter Of An Annulus : ALPHA Maths Homework Exercise

Description : Area and perimeter of an annulus.

Discussion : An aunnulus ia a circle with a hollow inner circle. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 4 questions.

area A

perimeter p

diameter d

internal diameter id

The equations are :

A = π / 4 (d² - id²)

p = π (d + id)

d = √(4 A / π + id²)

id = p / π - d

where

d = diameter

id = internal diameter

A = area

p = perimeter (internal and external circumference)

ALPHA : Geometry : Circle 04 : Area And Perimeter Of A Semi Circle : ALPHA Maths Homework Exercise

Description : Area and perimeter of a semi circle.

Discussion : A semi circle is half of a circle, formed by disecting a circle with a straight line through the center. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 4 questions.

area A

perimeter p

diameter d from A

radius r from p

The equations are :

A = π r² / 2 = π d² / 8

p = (π + 2) r = (π / 2 + 1) d

d = √(8 A / π)

r = p / (π + 2)

where

d = diameter

r = radius = d / 2

A = area

p = perimeter

ALPHA : Geometry : Circle 05 : Area And Perimeter Of A Segment : ALPHA Maths Homework Exercise

Description : Area and perimeter of a segment.

Discussion : A segment is formed by cutting through a circle with a single straight line. A semi circle is a segment which is exactly half of the area of the cirlce. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 4 questions.

area A

perimeter p

diameter d from A

radius r from p

The equations are :

A = r² / 2 (theta - sin(theta)) = d² / 8 (theta - sin(theta))

p = r (theta + 2 sin(theta / 2)) = d (theta / 2 + sin(theta / 2))

d = √(8 A / (theta - sin(theta))

r = p / (theta + 2 sin(theta / 2))

where

d = diameter

r = radius = d / 2

theta = angle subtended by chord (θ)

A = area

p = perimeter

ALPHA : Geometry : Circle 06 : Area And Perimeter Of A Sector : ALPHA Maths Homework Exercise

Description : Area and perimeter of a sector.

Discussion : A segment is the area swept out by a radius rotating about the center through an angle theta. See figure Basic 2D Geometry : Circular Shapes

The homework exercise has 4 questions.

area A

perimeter p

diameter d from A

radius r from p

The equations are :

A = theta r² / 2 = theta d² / 8

p = r (theta + 2) = d (theta / 2 + 1)

d = √(8 A / theta)

r = p / (theta + 2)

where

d = diameter

r = radius = d / 2

theta = swept angle (θ)

A = area

p = perimeter

ALPHA : Geometry : Polygon 01 : Area And Perimeter Of A Square : ALPHA Maths Homework Exercise

Description : Area and perimeter of a square.

Discussion : A square has four equal sides. Opposite sides of a square are parallel. All angles are right angles. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

base b from A

base b from p

The equations are :

A = b²

p = 4 b

b = &radic(A)

b = p / 4

where

b = base

A = area

p = perimeter

ALPHA : Geometry : Polygon 02 : Area And Perimeter Of A Rectangle : ALPHA Maths Homework Exercise

Description : Area and perimeter of a rectangle.

Discussion : A rectangle has two sets of equal parallel sides. All angles are right angles. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

base b from A and h

height h from p and b

The equations are :

A = b h

p = 2 (b + h)

b = A / h

h = p / 2 - b

where

b = base

h = height

A = area

p = perimeter

ALPHA : Geometry : Polygon 03 : Area And Perimeter Of A Kite : ALPHA Maths Homework Exercise

Description : Area and perimeter of a kite.

Discussion : A kite has two sets of equal sides which are adjacent. Opposite angles are equal. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

base b from A and h

side a from p and b

The equations are :

A = w h / 2

p = 2 (a + b)

w = 2 A / h

a = p / 2 - b

where

w = width

h = height

a b = sides

A = area

p = perimeter

ALPHA : Geometry : Polygon 04 : Area And Perimeter Of A Triangle : ALPHA Maths Homework Exercise

Description : Area and perimeter of a triangle.

Discussion : A triangle has three sides. An equilateral triangle has three equal sides and all three angles are equal. An isoceles triangle has two equal sides and two equal angles. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

base b

side a

The equations are :

A = b h / 2

p = a + b + c

b = 2 A / h

a = p - (a + b)

where

h = height

a b c = sides (b = base)

A = area

p = perimeter

ALPHA : Geometry : Polygon 05 : Area And Perimeter Of A Rhombus : ALPHA Maths Homework Exercise

Description : Area and perimeter of a rhombus.

Discussion : A rhombus has four equal sides. Opposite sides are parallel and opposite angles are equal. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

height h

base b

The equations are :

A = b h

p = 4 b

h = A / b

b = p / 4

where

b = base

h = height

A = area

p = perimeter

ALPHA : Geometry : Polygon 06 : Area And Perimeter Of A Parallelogram : ALPHA Maths Homework Exercise

Description : Area and perimeter of a parallelogram.

Discussion : A parallelogram has two sets of equal parallel sides. Opposite angles are equal. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

height h

side a

The equations are :

A = b h

p = 2 (a + b)

h = A / b

a = p / 2 - b

where

a b = sides (b = base)

h = height

A = area

p = perimeter

ALPHA : Geometry : Polygon 07 : Area And Perimeter Of A Trapezoid : ALPHA Maths Homework Exercise

Description : Area and perimeter of a trapezoid.

Discussion : A trapezoid has one pair of parallel sides. See figure Basic 2D Geometry : Polygon Shapes

The homework exercise has 4 questions.

area A

perimeter p

height h

side a

The equations are :

A = h (b + d) / 2

p = a + b + c + d

h = 2 A / (b + d)

a = p - (b + c + d)

where

a b c d = sides (b = base)

h = height

A = area

p = perimeter

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