Question

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

and AC = 6cm.

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Answer 1

Correct Question :

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

Given :

• AB = 3 cm.
• BC = 4 cm.
• CD = 4cm.
• DA = 5 cm.
• AC = 5 cm.

To Find :

• Area of Quadrilateral .

Solution :

In Δ ADC :

• a = 5 cm
• b = 4 cm
• c = 5 cm

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

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

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

$\longmapsto\tt\bf{s=7\:cm}$

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

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

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

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

$\longmapsto\tt\bf{2\sqrt{21}{cm}^{2}}$

In Δ ACB :

• a = 3 cm
• b = 4 cm
• c = 5 cm

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

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

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

$\longmapsto\tt\bf{s=6\:cm}$

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

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

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

$\longmapsto\tt{\sqrt{3\times{2}\times{3}\times{2}}}$

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

$\longmapsto\tt\bf{6\:{cm}^{2}}$

Now ,

$\longmapsto\tt{Total\:Area=6+2\sqrt{21}}$

$\longmapsto\tt\bf{15.1\:{cm}^{2}}$

So , The Area of Quadrilateral is 15.1 cm²...

Answer 2

Answer:

★ Given :

• AB = 3cm
• BC = 4cm
• CD = 4cm
• AD = 5cm
• AC = 5cm

★ To find :

• Area of quadrilateral .

★ Solution :

→ In ∆ADC :

• A = 5cm
• B = 4cm
• C = 5cm

$\sf{\ s = \frac {A + B + C }{2}}$

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

$\sf{s = \cancel\dfrac {14}{2}}$

$\sf{s = 7cm }$

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

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

$\sf{\sqrt {7×2×3×2}}$

$\sf{ 2 \sqrt{7×3}}$

$\sf{ 2 \sqrt{21} cm² }$

→ In ∆ACB

• A = 3cm
• B = 4cm
• C = 5cm

$\sf{s = \frac{ A + B + C }{2}}$

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

$\sf{ s = \cancel\dfrac {12}{2}}$

$\sf{ s = 6cm }$

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

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

$\sf{\sqrt { 6×3×2×1}}$

$\sf{\sqrt {3×2×3×2}}$

$\sf{2×3}$

$\sf{ → 6cm² }$

★ Now ;

$\sf{ Total \: area = 6 + 2 \sqrt {21}}$

$\sf{ → 15.1 cm² }$

So , the area of quadrilateral will be 15.1 cm² .