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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

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    Section : A
  • Qstn #1
    State which of the following are polygons:

    If the given figure is a polygon, name it as convex or concave.
    Ans : Only Fig. (ii), (iii) and (v) are polygons.
    Fig. (ii) and (iii) are concave polygons while
    Fig. (v) is convex.
  • Qstn #2
    Calculate the sum of angles of a polygon with :
  • #2-i
    10 sides
    Ans : No. of sides n = 10
    sum of angles of polygon = (n - 2)×180°
    = (10 - 2)× 180° = 1440°
  • #2-ii
    12 sides
    Ans : no. of sides n = 12
    sum of angles = (n - 2)×180°
    = (12 - 2)×180° = 10×180° = 1800°
  • #2-iii
    20 sides
    Ans : n = 20
    Sum of angles of Polygon = (n - 2)× 180°
    = (20 - 2)× 180° = 3240°
  • #2-iv
    25 sides
    Ans : n = 25
    Sum of angles of polygon = (n - 2)× 180°
    = (25 - 2)× 180° = 4140°
  • Qstn #3
    Find the number of sides in a polygon if the sum of its interior angles is :
  • #3-i
    900°
    Ans : Let no. of sides = n
    Sum of angles of polygon = 900˚(n - 2) × 180˚ = 900˚
    ⇒ n - 2 = 900/180
    ⇒ n - 2 = 5
    ⇒ n = 5 + 2
    ⇒ n = 7
  • #3-ii
    1620°
    Ans : Let no. of sides = n
    Sum of angles of polygon = 1620Ëš
    (n - 2) × 180˚ = 1620˚
    ⇒ n - 2 = 1620/180
    ⇒ n - 2 = 9
    ⇒ n = 9 + 2
    ⇒ n = 11
  • #3-iii
    16 right-angles
    Ans : Let no. of sides = n
    Sum of angles of polygon = 16 right = 16 × 90 = 1440˚
    (n - 2) × 180˚ = 1440˚
    ⇒ n - 2 = 1440/180˚
    ⇒ n - 2 = 8
    ⇒ n = 8 + 2
    ⇒ n = 10
  • #3-iv
    32 right-angles.
    Ans : Let no. of sides = n
    Sum of angles of polygon = 32 right angles = 32 × 90 = 2880˚
    (n × 2) × 180˚ = 2880
    n - 2 = 2880/180
    n - 2 = 16
    n = 16 + 2
    n =18
  • Qstn #4
    Is it possible to have a polygon; whose sum of interior angles is :
  • #4-i
    870°
    Ans : Let no. of sides = n
    Sum of angles = 870°
    (n - 2) × 180° = 870°
    ⇒ n - 2 = 870/180
    ⇒ n - 2 = 29/6
    ⇒ n = 29/6 + 2
    ⇒ n = 41/6
    Which is not a whole number.
    Hence it is not possible to have a polygon, the sum of whose interior angles is 870°
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