MathematicsCalculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm,  ∠A= 90 ∘   and BC = CD = 52 cm.

Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm,  A= 90   and BC = CD = 52 cm.


  1. A
  2. B
  3. C
  4. D
     

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    Solution:

    Let the diagram of the situation be,
    seoGiven that, AB = 32 cm, AD = 24 cm,  A= 90   and BC = CD = 52 cm.
    Apply the Pythagoras theorem, find the value of BD, and we have
    B D 2 =A B 2 +A D 2 B D 2 = 32 2 + 24 2 BD= 1600 BD=40cm  
    The area of the right-angled triangle ABD is given by,
    A ABD = 1 2 ×AB×AD = 1 2 ×32×24 =384c m 2  
    To find the area of the other triangle ACD, its perimeter is half of the perimeter.
    s= P 2 = a+b+c 2 = 52+52+40 2 = 144 2 =72cm  
    The area of the triangle is given by,
    A ACD = s(sa)(sb)(sc) = 72(7252)(7252)(7240) = 72(20)(20)(32) =960c m 2  
    Hence, the area of the quadrilateral is given by,
    A= A ABD + A ACD =384+960 =1344c m 2  
    Hence, the correct option is 1.
     
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