To find area of any general quadrilateral,

We split it into triangles and add their area parallelogram has opposites sides equal & parallel

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For Quadrilateral ABCD

We join AC

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So, we have two triangles - Δ ADC and Δ ABC

Let h 1 be height from point D to AC 

   & h 2 be height from point B to AC

 

So,

Area of Quadrilateral ABCD

  = Area of Δ ADC + Area of Δ ABC

  = 1/2 × AC × h 1 + 1/2 × AC × h 2

  = 1/2 × AC × (h 1 + h 2 )

  = 1/2 × (h 1 + h 2 )

where d = Length of Diagonal

 

Find area of quadrilateral ABCD

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Given

Length of diagonal = d = 10 cm

Length of Perpendicular dropped on AC

         h 1 = 5 cm

     & h 2 = 3 cm

Now,

 Area of ABCD = d/2 (h 1 + h 2 )

   = 10/2 (5 + 3)

   = 10/2 × 8

     = 5 × 8

     = 40 cm 2

 

Area of quadrilateral = 40 cm 2

  1. Chapter 11 Class 8 Mensuration
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.