Question

n a triangle PQR, a quadrilateral ABCD
insribed in it. If QC=5cm , CR= 3cm ,BR=4cm , PB=6cm, PA=5cm, AD=3cm and QD=2cm then find the area of quadrilateral ABCD?​

Answer 1

Answer:

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Answer 2

Area of the ΔPQR = √(14×6×4×4) = 8√21

By using sin formula for area = 1/2abSinθ

Ratio of area of ΔAPB and ΔPQR = 5×6/10×10 = 30/100 = 3/10 = 3×8/10×8 = 24/80

Ratio of area of ΔQDC and ΔPQR = 5×2/10×8 = 10/80

Ratio of area of ΔBRC and ΔPQR = 3×4/10×8 = 12/80

So the ratio of area of □ABCD and ΔPQR = (80 - 24 - 10 - 12)/80 = 34/80

Now the area of 80 unit ΔPQR = 8√21

So 1 unit = 8√21/80 = √21/10

So the area of 34 unit □ABCD = 34×√21/10

= 17√21/5 Ans.