Find the area of quadrilateral ABCD where AB = 7cm, BC=6cm,CD =12cm, DA=15cm and AC=9cm
Answers
Answer:
Step-by-step explanation:
Area of quadrilateral = area of triangle ABC + area of triangle ACD
since area of triangle = √s(s-a)(s-b)(s-c)
s= a+b+c/2
triangle abc
a=7 cm b= 6 cm c= 9 cm
=7+6+9/2
= 11
=√11(11-7)(11-6)(11-9)
=√11*4*5*2
=√440
=20.97 cm²
Triangle ACD
a= 15 b=12 c=9
s= 15+12+9/2
=18
=√18 (18-15)(18-12)(18-9)
=√18*3*6*9
=√2916
= 54 cm²
Area of quadrilateral = 20.97+54
=74.97 cm²
Answer:
Step-by-step explanation:
Best Answer
area of quadrilateral ABCD= Area of triangle ABC + Area of triangle ADC
Area of trianlge= sqrt(s(s-a)(s-b)(s-c))
FOR area of triangle ABC
s=(7+6+9)/2=11
area of triangle ABC=sqrt(11(11-7)(11-6)(11-9))
=sqrt(440)
= 20.9761
similarly,
area of triangle ADC=54
therefore area of quadrilateral ABCD=20.9761+ 54
=74.9761
ANOTHER WAY...
let it be 2 triangles rather than 1 big quadrilateral.
ABC = 7/6/9 and ADC = 15/12/9
total area
= √(11 * 4 * 5 * 2) + (12 * 9) / 2
= 2√110 + 54
= 74.976177
=~ 75 cm^2