Question

find the area of a 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:

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}2a+b+c

s=  \frac{48+14+50}{2}248+14+50

s= \frac{112}{2}2112

s= 56 cm

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

=  \sqrt{56(56-48)(56-14)(56-50)}56(56−48)(56−14)(56−50)

=\sqrt{56\times 8\times42\times6}56×8×42×6

= \sqrt{112896}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}2a+b+c

s=  \frac{112+78+50}{2}2112+78+50

s=  \frac{240}{2}2240

s= 120 cm

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

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

= \sqrt{120(8)(42)(70)}120(8)(42)(70)

=\sqrt{2822400}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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