Question

The three sides of a cyclic quadrilateral are 4cm 8cm and 6cm if the semi perimeter of a quardrilateral is 14cm find the area of the quadrilateral

Answer 1

Answer:

8√30 cm²

Step-by-step explanation:

Hi,

Given 3 sides of the quadrilateral are 4 cm, 8 cm and 6 cm.

Also, given the semi perimeter of a quadrilateral = 14 cm.

If a,b,c and d are sides of quadrilateral , semi perimeter 's' is given by

s = (a + b + c + d)/2.

Now, a = 4 b = 8 and c = 6

=> s = (18 + d)/2

=> d = 10 cm.

Using Brahmagupta's formula , Area of a cyclic quadrilateral is given by

√(s-a)(s-b)(s-c)(s-d)

=> A = √(14-4)(14-8)(14-6)(14-10)

=√10*6*8*4

=√1920

=8√30 cm².

Hope, it helped !

Answer 2

Answer:

43.8 sq cm

Step-by-step explanation:

Given The three sides of a cyclic quadrilateral are 4cm 8cm and 6cm if the semi perimeter of a quardrilateral is 14cm, to find the area of the quadrilateral

 The semi perimeter of a quadrilateral is given by 14 cm. So

        S = a + b + c + d / 2

        14 = 4 + 8 + 6 + d / 2

      18 + d = 28

         d = 10 cm

So now we need to find area of a quadrilateral. So area

      A = √(s -a)(s - b)(s - c)(s - d)

      A = √(14 - 4)(14 - 8)(14 - 6)(14 - 10)

       A = √10 x 6 x 8 x 4

       A = √1920

      A = 43. 81 sq cm

Area of a quadrilateral is 43.81 sq cm