Question

In a quadrilateral ABCD,Ab=28cm,Bc=26cm,Cd=50cm,Da=40cm and diagonal Ac=30cm find the area of the quadrilateral

Answer 1

this will help you......

Answer 2

So, Area of the Quadrilateral $ABCD=936 cm^{2}$

Step-by-step explanation:

Given;

For a quadrilateral $ABCD$,

$AB=28$cm , $BC=26$cm , $CD=50$cm , $DA=40$cm and diagonal $AC=30$

From figure,

By Heron's formula;

Area of $\bigtriangleup ABC=\sqrt{s(s-a)(s-b)(s-c)}$  Where $s=\frac{a+b+c}{2}$

So,

  $s=\frac{28+26+30}{2}$

⇒$s=42$

Now,

  Area of $\bigtriangleup ABC=\sqrt{42(42-28)(42-26)(42-30)}$

⇒Area of $\bigtriangleup ABC=336$ $cm^{2}$

Similarly;

By Heron's formula;

Area of $\bigtriangleup ADC=\sqrt{s(s-a)(s-b)(s-c)}$  Where $s=\frac{a+b+c}{2}$

So,

  $s=\frac{40+50+30}{2}$

⇒$s=60$

Now,

Area of $ADC=\sqrt{60(60-40)(60-50)(60-30)}$

Area of $ADC=600$ $cm^{2}$

  Area of the Quadrilateral $ABCD=$ Area of $\bigtriangleup ABC$$+$ Area of $\bigtriangleup ADC$

⇒Area of the Quadrilateral $ABCD=$$(336+600)$ $cm^{2}$

∴ Area of the Quadrilateral $ABCD=936 cm^{2}$