Question

Find the area of a quadrilateral ABCD in which AB = 8 cm, BC = 6 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm

Answer 1

$24 + 8 \sqrt{21}$

Answer 2

Answer:

Quadrilateral ABCD is divided by diagonal AC in to 2Triangles

ABC &ACD .AC DIAGONAL is common to both of them For both Triangles all the sides are known.

a =6 b=10 c=8 ; semi perimeter =[6+10+8]/2 =24/2 =12cm

Area ={s{s-a][s-b][s-c]} 1/2

Area =[12[12-6][12-10][12-8]]1/2=[12[6*2*4]]1/2

=[[12*12][4]]1/2= 12*2 =24 sq cms

Now triangle ACD

semi perimeter =[10+10+8]/2=28/2 =14

Area of Triangle ACD={14[14-10][14-10][14-8]}1/2

{14*4*4*6}1/2 =4{84}1/2 =4*9.17 =36.67 sqcm

Area of Triangle ACD =36.67 sqcm

Area of Quadrilateral =Area of triangleABC+ Area of triangleACD=24+36.67 =60.67 sqcms

Answer: Area of Quadrilateral=60.67 sqcms