Question

Q17. what is the area of quadrilateral
ABCD in which AB =3 cm, BC = 4 cm,
CD = 4 cm, DA = 5 cm and AC = 5 cm.​

Answer 1

Answer:-

Area of the Quadrilateral = area of ꕔABC + area of ꕔADC

Area of ꕔABC [ using heron's formula ]

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

{where s is the semi perimeter}

$s = \frac{a + b + c}{2}$

$= \frac{3 + 4 + 5}{2}$

$= { \dfrac{ \cancel{12} {}^{ \: \: \: \: 6} }{ \cancel{2}_{ \: \: \: \: 1}}}$

$= 6$

Area of ꕔ ABC = $\sqrt{s(s - a)(s - b)(s - c)}$

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

$= \sqrt{6 \times 3 \times 2 \times 1}$

$= \sqrt{6 \times 6}$

= 6 cm²

Area of ꕔADC

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

{where s is the semi perimeter}

$s = \frac{a + b + c}{2}$

$= \frac{5 + 4 + 5}{2}$

$= { \dfrac{ \cancel{14} {}^{ \: \: \: \: 7} }{ \cancel{2}_{ \: \: \: \: 1}}}$

$= 7$

Area of ꕔ ADC = $\sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{7(7 - 5)(7 - 4)(7 - 5)}$

$= \sqrt{7 \times 2 \times 3 \times 2}$

$= \sqrt{2 \times 2 \times 7 \times 3}$

$= 2\sqrt{21}$

$= 2 \times 4.58$

= 9.16 cm²

Area of the Quadrilateral = area of ꕔABC + area of ꕔADC

Area of the Quadrilateral = 6 + 9.16

= 15.16 cm² (approx)

Answer : The area of the quadrilateral is 15.16 cm²

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Answer 2

hope it helps you......