Question

find the area of quadrilateral abcd in which ab=9cm bc=12cm cd=5cm da=8cm and c=90° ​

Answer 1

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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TAUTIK