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Find the Area of the Quadrilateral Abcd in Which in Ab=42 Cm, Bc=21 Cm, Cd=29cm, Da=34 Cm and Diagonal Bd = 20 Cm. - Mathematics

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Find the area of the quadrilateral ABCD in which in AB=42 cm, BC=21 cm, CD=29cm, DA=34 cm and diagonal BD = 20 cm. 

 

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Solution

Area of ΔABD=`sqrt(s(s-a)(s-b)(s-c))` 

                   `s=1/2(a+b+c)` 

                   `s=(42+20+34)/2` 

                   `s= 48 cm` 

Area  of ` ΔABD=sqrt(48(48-42)(48-20)(48-34))` 

                      =`sqrt(48xx6xx28xx14)` 

                     =`sqrt(112896)` 

                      =`336 cm^2` 

Area of` Δ BDC=sqrt(s(s-a)(s-b)(s-c))` 

                      s=`1/2 (a+b+c)` 

                      s=`(21+20+29)/2` 

                      s=`35 cm` 

Area of  Δ BDC= `sqrt(35(35-29)(35-20)(35-21))` 

                       =`sqrt(35xx6xx15xx14)` 

                     = `sqrt(44100)` 

                     =`210cm^2` 

∴ Area of quadrilateral ABCD = Area of ΔABD+ Area of ΔBDC   

=`336+210` 

=`546cm^2`

Concept: Area of Circle
  Is there an error in this question or solution?

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 17 Perimeter and Areas of Plane Figures
Q 27

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