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ICSE-VIII-Mathematics

20: Area of Trapezium and a Polygon Class 8 Maths

with Solutions - page 5
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  • #11
    A thin metal iron-sheet is rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m2.
    Also, find the distance between the opposite sides of this rhombus.
    Ans : Side of rhombus shaped iron sheet = 10 m and one diagonals (AC) = 16 m
    Join BD diagonal which bisects AC at O
    The diagonals of a rhombus bisect each other at right angle
    ∴ AO = OC = 16/2 = 8 m
    Now in right ΔAOB
    AB2 = AO2 + BO2
    ⇒ (10)2 = (8)2 + BO2
    ⇒ 100 = 64 + BO2
    ⇒ BO2 = 100 - 64
    = 36
    = (6)2
    ∴ BO = 6 m
    ∴ BD = 2 × BO
    = 2 × 6
    = 12 m
    Now, area of rhombus = (d1 × d2)/2
    = (16 × 12)/2
    = 96 m2
    Rate of pairing = ₹ 6 per m2
    ∴ Total cost of painting both sides = 2 × 96 × 6
    = ₹ 1152
    Distance between two opposite sides = Area/Base
    = 96/10
    = 9.6 m