Maths-
General
Easy

Question

In a Trapezium ABCD, as shown, A B parallel to D C comma A D equals D C equals B C equals 20 c m and angle equals 60 º then length of AB is

  1. 40 cm    
  2. 50 cm    
  3. 80 cm    
  4. 60 cm    

hintHint:

A convex quadrilateral having exactly one set of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. Here we have given a Trapezium ABCD where  A B parallel to D C comma A D equals D C equals B C equals 20 c m and angle equals 60 º , we have to fond the length of AB.

The correct answer is: 40 cm


    Now we know that a quadrilateral with one set of parallel opposite sides is a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. It also goes by the name trapezoid. The parallelogram is occasionally referred to as a trapezoid with parallel sides.
    Here we have given trapezium ABCD as:

    A B parallel to D C comma A D equals D C equals B C equals 20 c m space a n d space angle A equals 60 º.
L e t s space d r a w space a space p e r p e n d i c u l a r space l i n e space f r o m space D comma space t o u c h i n g space A B A space a t space p o i n t space P. space I t space w i l l space f o r m space a space t r i a n g l e space A P D.
N o w space i n space t r i a n g l e space A P D comma space w e space h a v e colon
cos space 60 degree equals fraction numerator A P over denominator A D end fraction
1 half equals fraction numerator A P over denominator 20 end fraction
A P equals 10 space c m
N o w colon
left parenthesis 2 cross times A P right parenthesis plus D C equals A B
left parenthesis 2 cross times 10 right parenthesis plus 20 equals 40 space c m

    Here we used the concept of trapezium and parallel lines. A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other. Here the length of AB is 40 cm.

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