Question

Find the area of a quadrilateral ABCD in which AB = 3cm,BC=4cm,CD=4cm,DA=5cm and AC=5cm.

Answer 1

✯✯ QUESTION ✯✯

Find the area of a quadrilateral ABCD in which AB = 3cm,BC=4cm,CD=4cm,DA=5cm and AC=5cm..

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✰✰ ANSWER ✰✰

✔In Δ ADC : -

• a = 5cm
• b = 4cm
• c = 5cm

$\implies\tt{s=\dfrac{a+b+c}{2}}$

$\implies\tt{s=\dfrac{5+4+5}{2}}$

$\implies\tt{s=\cancel\dfrac{14}{2}}$

$\implies\tt\bold{s=7cm}$

➥Now ,

$\implies\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\implies\tt{\sqrt{7(7-5)(7-4)(7-5)}}$

$\implies\tt{\sqrt{7\times{2}\times{3}\times{2}}}$

$\implies\tt{2\sqrt{7\times{3}}}$

$\implies\tt{2\sqrt{21}}$

$\implies\tt\bold{9.1{cm}^{2}}$

_______________________

✔In Δ ACB : -

• a = 3cm
• b = 4cm
• c = 5cm

$\implies\tt{s=\dfrac{a+b+c}{2}}$

$\implies\tt{s=\dfrac{3+4+5}{2}}$

$\implies\tt{s=\cancel\dfrac{12}{2}}$

$\implies\tt\bold{s=6cm}$

➥Now ,

$\implies\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\implies\tt{\sqrt{6(6-3)(6-4)(6-5)}}$

$\implies\tt{\sqrt{6\times{3}\times{2}\times{1}}}$

$\implies\tt{\sqrt{2\times{3}\times{3}\times{2}\times{1}}}$

$\implies\tt{2\times{3}}$

$\implies\tt\bold{6{cm}^{2}}$

_______________________

$\implies\tt\bold{Total\:Area=9.1+6}$

$\implies\tt\boxed{15.1{cm}^{2}}$