find the area of quadrilateral abcd in which ab=9cm bc=12cm cd=5cm da=8cm and c=90°
Answers
Answer:
66 cm²
Step-by-step explanation:
First draw a diagonal BD.
Now in ∆BCD,
BC = 12 cm
CD = 5 cm
BD = √BC²+CD²
= √12²+5²
= √144+25
= √169
= 13 cm
Therefore, BD = 13 cm
Now,
ar(BCD) = ½×b×h
= ½×5×12
= 30 cm²
In ∆ABD,
a = 8 cm
b = 9 cm
c = 13 cm
s(Semi-Perimeter) = a+b+c/2
= 8+9+13/2
= 30/2
= 15 cm
Therefore,
ar(ABD) = √s(s-a)(s-b)(s-c)
= √15(15-8)(15-9)(15-13)
= √15×7×6×2
= √3×5×7×3×2×2 (Since 15=3×5 & 6=3×2)
= √3×3×2×2×7×5
=3×2 √7×5
= 6 × √35
= 6×6 (Since √36= 6 and √35 is close to √36 )
= 36 cm²
Therefore,
ar(ABCD) = ar(BCD) + ar(ABD)
= 30+36
= 66 cm² approx.
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