Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 3K views

    KKKKKKKK

    Uploaded by

    Jeny Ross Javier Malabanan
    1) The document discusses different shapes involving circles such as sectors, segments, and figures bounded by or inscribed in circles. 2) Examples provide calculations to find areas and perimeters of composite figures made of combinations of circles, triangles, trapezoids, and squares. 3) Key formulas discussed include those for finding the area of circles, sectors, triangles, trapezoids, and composite figures combining different shapes.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd

    KKKKKKKK

    Uploaded by

    Jeny Ross Javier Malabanan
    3K views14 pages
    1) The document discusses different shapes involving circles such as sectors, segments, and figures bounded by or inscribed in circles. 2) Examples provide calculations to find areas and perimeters of composite figures made of combinations of circles, triangles, trapezoids, and squares. 3) Key formulas discussed include those for finding the area of circles, sectors, triangles, trapezoids, and composite figures combining different shapes.

    Original Description:

    Original Title

    kkkkkkkk

    Copyright

    © Attribution Non-Commercial (BY-NC)

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    1) The document discusses different shapes involving circles such as sectors, segments, and figures bounded by or inscribed in circles. 2) Examples provide calculations to find areas and perimeters of composite figures made of combinations of circles, triangles, trapezoids, and squares. 3) Key formulas discussed include those for finding the area of circles, sectors, triangles, trapezoids, and composite figures combining different shapes.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    3K views14 pages

    KKKKKKKK

    Uploaded by

    Jeny Ross Javier Malabanan
    1) The document discusses different shapes involving circles such as sectors, segments, and figures bounded by or inscribed in circles. 2) Examples provide calculations to find areas and perimeters of composite figures made of combinations of circles, triangles, trapezoids, and squares. 3) Key formulas discussed include those for finding the area of circles, sectors, triangles, trapezoids, and composite figures combining different shapes.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 14
    At a glance
    Powered by AI
    The passage discusses examples of geometry problems involving quadrilaterals, circles, and their properties. Quadrilaterals examples include finding the area of a parallelogram and the difference between two trapezoids. Circle examples include finding areas bounded by concentric circles and regions within or bounded by circles.

    Examples of problems involving quadrilaterals include finding the area of a parallelogram with given dimensions, and finding the area of the difference between two isosceles trapezoids.

    Examples of problems involving circles include finding the area between two concentric circles with given radii, finding the area of a triangle inscribed in a circle, and finding the area of a square inscribed in a circle.

    Quadrilaterals

    Example 1. A city block is in the form of a parallelogram whose shorter


    diagonal AB is perpendicular to side BC, as shown in the figure. The
    shorter sides represent streets and the longer sides represent avenues. If
    the distance between the avenues is 400ft and the length of each street is
    500 ft, find the area of the block.
    Quadrilaterals
    2 2
    500 400 DC =
    400
    500 300
    2000
    3
    AB
    AB
    =
    =
    ( ) ( )
    2000
    500 333333.33 . 37037.04 . .
    3
    BC AB sq ft or sq yd
    | |
    = =
    |
    \ .
    Quadrilaterals
    Example 2. Find the area of the rectilinear figure shown, if it is the
    difference between two isosceles trapezoids whose corresponding sides
    are parallel.
    Quadrilaterals
    ( )
    3
    8 6
    3 6
    2.25
    8
    z
    z
    =
    = =
    ( )( ) ( ) ( ) ( ) ( ) ( )
    1 1
    12 18 8 18 2 2.25 2.136 18 2 2.136 6 51.132
    2 2
    A sqin
    (
    = + + + =

    2 2
    3 8 73 y = + =
    8 2
    73
    2 73
    2.136
    8
    x
    x
    =
    = =
    Circles
    Area = x radius
    2
    = /4 x diameter
    2
    2
    1 1
    2 2
    A RC R u = =
    2 2
    4
    A r D
    t
    t = =
    2 C R D t t = =
    Circumference = 2 x radius = x diameter
    Area = 1/2 x radius
    x
    arc
    Area = Area of sector Area of triangle
    1 1
    2 2
    A RC ba =
    Sector of a circle:
    Segment of a circle:
    Circle
    Example 1. The section of a certain solid is bounded by two concentric
    circles whose radii are 6.1 ft and 4.1 ft. Find the area of this section.
    ( )
    ( )
    ( ) ( ) ( ) ( )
    ( )( ) ( )( )
    2
    1
    2
    2
    2 2 2 2
    1 2
    6.1
    4.1
    6.1 4.1 6.1 4.1
    6.1 4.1 6.1 4.1 10.2 2 64.089
    A
    A
    A A
    sq ft
    t
    t
    t t t
    t t
    =
    =
    (
    = =

    = + = =
    Circles
    Example 2. A triangle is inscribed in a circle of radius 6 inches as
    shown in the diagram. What is the area of the shaded polygon?
    ( )( )
    1 1
    5 12 30
    2 2
    A bh in = = =
    If a triangle is inscribed in a circle with the
    diameter as one side, it will always be a
    right triangle.
    Circles
    Example 3. A square is inscribed in a circle of 10 .What is the area of the
    shaded region?
    10
    10
    P C d
    d
    t t = = =
    =
    2 2 2
    2
    2
    10
    2 100
    50
    7.07
    x x
    x
    x
    x units
    + =
    =
    =
    ~
    ( )
    ( )
    2
    2
    2
    2
    2
    7.07 50
    5 25
    25 50 28.5
    square
    circle
    circle square
    A x
    A r
    A A unit
    t t t
    t
    = = =
    = = =
    = ~
    Circles
    Example 4. Find the perimeter and area enclosed by the track ABCDEF in the
    figure?
    ( )( ) ( ) ( )
    2 440 2 2 70 440 2 1319.82 Total Perimeter r ft t t = + = + =
    ( ) ( )( )
    2
    2
    70 440 70 2 76993.804 Total Area r bh sq ft t t = + = + =
    Circles
    Example 5. Each of the four circles shown in the figure is tangent to the other
    three. If the radius of each smaller circle is a = 2.71, find the area of the
    largest circles.
    Circles
    2.71
    sin60
    3.13
    3.13 2.71 3.31 5.84
    x
    x
    radius a
    =
    =
    = + = + =
    ( )
    2
    2
    5.84 107.14 A r squnit t t = = =
    Circles
    Example 6. The plane area shown consists of an isosceles trapezoid (non-
    parallel sides equal) and a segment of a circle. If non-parallel sides are
    tangent to the segment at points A and B, find the area of the composite
    figure.
    Circles
    3 2
    cos60
    3"
    R
    R
    =
    =
    sin60
    3
    2.598"
    3 2.598 0.40"
    h h
    R
    h
    R h
    = =
    =
    = =
    ( ) ( ) ( )( )
    2
    2
    1 1 1 1
    3 60 3 2.598
    2 2 2 180 2
    4.712 3.897 0.815"
    segment of acircle
    segment of acircle
    A R ab
    A
    t
    u
    (
    | |
    = =
    |
    (
    \ .

    = =
    Circles
    4.6
    tan30
    7.967"
    x
    x
    =
    =
    ( ) ( )( )
    1 1
    3 18.934 4.6 50.45
    2 2
    trapezoid
    A a b h = + = + =
    ( )
    3 2 3 2 7.967 18.934" x + = + =
    0.815 50.45 51.265"
    total
    A = + =

    You might also like