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    4 Quadrilaterals 1

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    4 Quadrilaterals 1

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    4 Quadrilaterals 1

    Uploaded by

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    Copyright:

    © All Rights Reserved
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    of 20

    DifferEnt

    types
    of
    QUADRILATERALS
    Family of
    Quadrilaterals
    Quadrilaterals

    Parallelogram Trapezoid Trapezium

    Isosceles Right
    Rhombus Rectangle Trapezoid
    Trapezoid

    Square
    The Trapezium
    .B
    A. -A quadrilateral
    with no pair of
    parallel sides.
    D.
    .
    C
    Isosceles
    TRAPEZOID Trapezoid
    •Isosceles Trapezoid:
    a trapezoid whose
    nonparallel sides are
    congruent
    • One pair of opposite
    •The base angles of an
    sides are parallel isosceles trapezoid
    are congruent

    •The diagonals of an
    isosceles trapezoid
    are congruent
    PARALLELOGRAM

    • Opposite sides are equal


    • Opposite sides are parallel
    • Opposite angles are equal
    • Diagonals bisect each other
    RHOMBUS

    • All sides are equal


    • Opposite sides are parallel
    • Opposite angles are equal
    • Diagonals bisect each other at 90°
    RECTANGLE

    • Opposite sides are equal


    • Opposite sides are parallel
    • All angles are right angles (90o)
    • Diagonals are equal and bisect one another
    SQUARE

    • All sides are equal


    • Opposite sides are parallel
    • All angles are right angles (90o)
    • Diagonals are equal and bisect one
    another at right angles
    Parallelogram Rectangle
    P = 2a + 2b P = 2l + 2w
    A = bh A = lw
    A = ab sin 

    a e₁ w
    h
    Ɵ
    l
    b
    Square Trapezoid
    b1

    h
    b b2

    A = (b1 + b2 )h
    1
    P = 4b 2
    A = mh
    A=b 2
    b1 + b2
    m=
    2
    Rhombus
    2 2
     e1   e2 
    b =   + 
    2  2
    Ɵ
     e1 
     = 2 tan  
    −1

     e2 
    e₂
    P = 4b e₁
    1
    A = e1e2
    2 b
    A = bh
    A = b 2 sin 
    Examples
    1. An isosceles trapezoid has an area of 40 m2
    and an altitude of 2m. Its two bases have ratio of
    2:3. What are the lengths of the bases and one
    diagonal of the trapezoid?
    2. A piece of wire is shaped to enclose an
    equilateral triangle whose area is 36√3 cm2. It is
    then reshaped to enclose a rectangle whose
    length is 10 cm. Find the area of the rectangle.
    3. The area of a rhombus is 143 m2. If the longer
    diagonal is 26m, find the angle opposite the
    longer diagonal and the length of one side of the
    rhombus.
    Examples

    5. If the sides of the parallelogram and an


    includes angle are 9 m, 13 m, and 150⁰,
    respectively. Find the length of the shorter
    diagonal and the area of the parallelogram.
    Examples
    1. Find the area and the perimeter of the right
    trapezoid shown in the figure.
    8 cm

    60⁰

    11 cm

    2. The side of a square is x meters. The


    midpoints of its sides are joined to form
    another square whose area is 16 sq. meters.
    Find the value of x and the area of the
    portion of the bigger square that is outside
    the smaller square.
    Examples
    Exercise
    1. A certain city block is in the form of a
    parallelogram. Two of its sides measure 52 ft.
    and 71 ft. If the area of the land in the block is
    856 sq. ft., what is the length of its longer
    diagonal.
    2. A right trapezoid has an area of 180 sq. m. and
    an altitude of 5 m. Its two bases have a ratio of
    4:5. What are the lengths of the bases and the
    perimeter of the trapezoid?
    3. The area of a rhombus is 297 sq. m. If the
    diagonal is 53 m, find the angle opposite the
    shorter diagonal and the length of one side of
    the rhombus.
    Exercise
    1. Find the area and perimeter of a square whose
    diagonal is 21 units long.
    2. A certain city block is in the form of a
    parallelogram. Two of its sides measure 32 ft.
    and 41 ft. If the area of the land in the block is
    656 sq. ft., what is the length of its longer
    diagonal.
    3. A right trapezoid has an area of 180 sq. m. and
    an altitude of 5 m. Its two bases have a ratio of
    4:5. What are the lengths of the bases and the
    perimeter of the trapezoid?
    4. The area of a rhombus is 297 sq. m. If the longer
    diagonal is 53 m, find the angle opposite the
    shorter diagonal and the length of one side of
    the rhombus.
    Exercise
    1. The lengths of the sides of a triangle are in the ratio
    17:10:9. Find the lengths of the three sides if the area of the
    triangle is 576 square cm.
    2. In an acute triangle ABC, an altitude AD is drawn. Find the
    area of triangle ABC if AB=15 in., AC=18 in., and BD=10 in.
    3. A certain city block is in the form of a parallelogram. Two of
    its sides measure 32 ft. and 41 ft. If the area of the land in
    the block is 656 sq. ft., what is the length of its longer
    diagonal.
    4. A right trapezoid has an area of 180 sq. m. and an altitude
    of 5 m. Its two bases have a ratio of 4:5. What are the
    lengths of the bases and the perimeter of the trapezoid?
    5. The official ball diamond is in the form of a square. The
    distance between the home base and the second base in a
    baseball is usually 35 m. Find the area and the distances
    between the bases.
    1. The altitude BE of parallelogram ABCD divides the
    side AD into segments in the ratio 1:3. Find the area of
    the parallelogram if the length of its shorter side AB is
    14cm, and one of its interior angle measures 60°.

    2. A piece of wire is shaped to enclose an equilateral


    triangle in which the area is 16√3 cm². It is then
    reshaped to enclose a rectangle whose length is 9cm.
    Find the area of the rectangle.
    Assignment:
    (one whole yellow paper--by pair)
    1. A certain city block is in the form of a
    parallelogram. Two of its sides measure 81 ft.
    and 30 ft. If the area of the land in the block is
    1056 sq. ft., what is the length of its longer
    diagonal.
    2. A right trapezoid has an area of 156 sq. m. and
    an altitude of 8 m. Its two bases have a ratio of
    6:7. What are the lengths of the bases and the
    perimeter of the trapezoid?
    3. A rectangle and a square have the same area. If
    the length of the side of the square is 6 units
    and the longest side of the rectangle is 5 more
    than the measure of the shorter side. Find the
    dimensions (length and width) of the rectangle.

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