Question

Find the area of the Quadrilateral ABCD,given in the adjoining figure in which AB =14cm, BC=78CM, CD=112CM, BD=50CM and DA=48cm​

Answer 1

Step-by-step explanation:

Solving for Any Quadrilateral

Find the lengths of all four sides.

Find the angles between a and d and b and c.

Use the triangle area formula to find the area of the quadrilateral

Answer 2

The area of the quadrilateral ABCD is 2016 cm²

Step-by-step explanation:

In quadrilateral ABCD

given  AB =14cm, BC=78cm, CD=112cm, BD=50cm and DA=48cm​

we have to find the area of the quadrilateral

Area of quadrilateral  ABCD =  area of traingle ABD + area of traingle BCD

area of traingle ABD

using the heron's formula

sides of the traingle are a= 48 cm ,b= 14 cm, c= 50 cm

then

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

s=  $\frac{48+14+50}{2}$

s= $\frac{112}{2}$

s= 56 cm

area of traingle ABD= $\sqrt{s(s-a)(s-b)(s-c)}$

=  $\sqrt{56(56-48)(56-14)(56-50)}$

=$\sqrt{56\times 8\times42\times6}$

= $\sqrt{112896}$

= 336 cm²

area of triangle BCD

again using heron's formula

sides are a= 112 cm , b= 78 cm, c= 50 cm

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

s=  $\frac{112+78+50}{2}$

s=  $\frac{240}{2}$

s= 120 cm

area of traingle BCD = $\sqrt{s(s-a)(s-b)(s-c)}$

=$\sqrt{120(120-112)(120-78)(120-50)}$

= $\sqrt{120(8)(42)(70)}$

=$\sqrt{2822400}$

= 1680 cm²

now

Area of quadrilateral  ABCD =  area of traingle ABD + area of traingle BCD

Area of quadrilateral  ABCD= 336+ 1680

Area of quadrilateral  ABCD= 2016 cm²

hence, the area of the quadrilateral ABCD is 2016 cm²

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