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Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm AD = 9cm, CD = 12cm, ACB=900and AC = 15cm.


Solution

In right ΔABC,ACB=900
AB2=AC2+BC2

(17)2=(15)2+BC2

BC2=289225=64=(8)2
BC= 8 cm
Now Area of ΔABC,
= 12base×altitude
=12×8×15=60cm2
and area of Δ ADC,
s=a+b+c2=15+12+92=362=18
Area= s(sa)(sb)(sc)
=18(1815)(1812)(189)
= 18×3×6×9= 6×3×3×6×3×3
= 3×3×6=54cm2
Area of quadrilateral ABCD = 60+54
=114cm2
and perimeter = AB+BC+CD+DA
= 17+8+12+9=46 cm


Mathematics
RD Sharma
Standard IX

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