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    Hi, can anybody do this question?

    A is the point (8,0) and Bis the point (12,6)
    M and N are the midpoints of OA and OB respectively where O is the origin

    Calculate the area of trapezium ABMN

    Thanks
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    what syllabus is this from?
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    attatched is an elaborate diagram i drew.

    you need to find NM and AB using trig. then use A=1/2 (MN+AB) * height

    i've just got up so apologies if i'm off the mark.

    kiwi.
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    (Original post by manhunter)
    Hi, can anybody do this question?

    A is the point (8,0) and Bis the point (12,6)
    M and N are the midpoints of OA and OB respectively where O is the origin

    Calculate the area of trapezium ABMN

    Thanks
    The point M is (4,0)
    The point N is (6,3)
    The line AB is length root(4^2 + 6^2) = root52
    The line MN is length root(2^2 + 3^2) = root13
    equation of AB: y = 3x/2 + 8
    equation of MN: y = 3x/2 + 4

    for AB when y = 0
    -3x = 8
    x = -8/3

    for MN when y = 0
    -3x = 4
    x = -4/3

    perpendicular hight of trapezium is -4/3 - -8/3 = 4/3

    equation for area of trapezium is (side a +side b/2)*height

    root 52 = root4*root13 = 2root13
    area = 2root13*root13/2 * 4/3 = 26/2*4/3 = 52/3 = 17.3333... unit^2

    This doesn't look like usual P1 stuff but I think my answer is correct. Sorry I trundled through it so slowly.

    MB
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    Thanks Kiwi

    I got 18 - Subract the areas of the smaller triangles from the big triangle.
    It's quite easy when you draw a proper diagram; I was thinking of calculating the gradient of the perpendicular to MN which goes through A, to find the height; and then use the formula, by calculating lengths MN and AB

    btw I am doing the Edexcel board
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    ****, my perpendicular height is wrong. Sorry.

    MB
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    (Original post by musicboy)
    equation for area of trapezium is (side a +side b/2)*height
    not entirely correct, you need the half outside the brackets:

    eg: side a = 4, side b = 2

    4+2/2 = 5
    (4+2)/2 = 3

    better explained than mine though
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    hehe, the easy methods are often overlooked.

    ps: technically it's square units not cm^2, although i doubt you'd lose any marks for it; just good practise.

    where did your answer go?
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    Area of trapezium = Area of large triangle - (Area of 2 smaller triangles)
    = 36 - (12 + (9-3))
    = 18 cm^2
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    I'll concur with 18 square units.

    IMHO the simplest way to do it is to draw the trapezium and then draw a rectangle round it (vertices: (4,0), (12,0), (4,6), (12,6)). This leaves you with two right-angled triangles and a regular trapezium outside the trapezium in question, all of which have integer areas. Then simply subtract the sum of these areas from the area of the rectangle to get 18.
 
 
 
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