Question

If a b is equal to 14 centimetre bc is equal to 13 cm cd is equal to 17 cm da is equal to 8 cm and ac is equal to 15 cm then find the area of quadrilateral abcd

Answer 1

Answer:

Step-by-step explanation:

here we can use the heron's formula,

in ΔABC,

first we need to find the semi perimeter of ABC,

S=14+15+13/2

 =21

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

      = $\sqrt{(21)(21-13)(21-14)(21-15)}$

       = $\sqrt{(21)(8)(9)(10)}$

       = $12\sqrt{105}$

in ΔADC,

S = 8+15+17/2

  = 20

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

       = $\sqrt{(20)(20-8)(20-15)(20-17)}$

       = $\sqrt{(20)(12)(5)(3)}$

       = 60

area of quadrilateral ABCD = area(ABC) + area(ADC)

                                             = $12\sqrt{105}$ + 60

                                             = 12($\sqrt{105}$ + 5)