Question

Find area of a quadrilateral ABCD in which ab=3cm bc=4cm cd=4cm da=5cm and ac=5cm.Find area of a quadrilateral ABCD in which ab=3cm bc=4cm cd=4cm da=5cm and ac=5cm.Find area of a quadrilateral ABCD in which ab=3cm bc=4cm cd=4cm da=5cm and ac=5cm.

Answer 1

CORRECT QUESTION:

Find area of a quadrilateral ABCD in which ab=3cm bc=4cm cd=4cm da=5cm and ac=5cm

GIVEN:

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

TO FIND:

• What is the area of quadrilateral ?

SOLUTION:

We have given that AB = 3 cm, BC = 4 cm and AC = 5 cm

Right angled at B ∴ ∠B = 90°

So, ∆ABC is a right angled triangle

We know that, the formula for finding the area of ∆ABC is:-

$\large\bf{ Area = \dfrac{1}{2} \times base \times height}$

According to question:-

$\rm{\rightharpoonup Area = \dfrac{1}{\cancel{2}} \times 3 \times \cancel{4}}$

$\rm{\rightharpoonup Area = 3 \times 2}$

$\bf{\rightharpoonup \: \star \: Area = 6 \: cm^2 \: \star }$

❝ Area of ∆ABC is 6 cm² ❞

Now, we have to find the area of ∆ACD

☞To find the area of ∆ACD, we use the Heron's formula

• $\bf{ a = 4 \: cm}$
• $\bf{ b = 5 \: cm}$
• $\bf{ c = 5 \: cm}$

$\bf{ \rightharpoonup s = \dfrac{ a + b + c}{2}}$

$\rm{\rightharpoonup s = \dfrac { 4+5+5}{2}}$

$\rm{\rightharpoonup s = \cancel\dfrac{14}{2}}$

$\bf{ \star \: s = 7 \: cm\: \star }$

∴ Area of ∆ACD,

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

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

$\rm{\rightharpoonup Area = \sqrt{ 7 \times 3 \times 2 \times 2}}$

$\rm{\rightharpoonup Area = \sqrt{ 84}}$

$\rm{\rightharpoonup Area = 2\sqrt{21}\: cm^2}$

➤ √2 = 4.6 (approx)

$\rm{ \rightharpoonup 2 \times 4.6}$

$\bf{ \rightharpoonup \: \star \: Area = 9.2 \: cm^2\: \star }$

❝ Area of ∆ACD is 9.2 cm² ❞

⚫ Area of Quadrilateral ABCD = Area of ∆ABC + Area of ∆ACD

$\rm{ \rightharpoonup Area = 6 + 9.2 }$

$\bf{ \rightharpoonup \: \star \: Area = 15.2 \: cm^2\: \star }$

❝ Area of Quadrilateral = 15.2 cm² ❞

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