Question

the sides of a quadrilateral ABCD are AB =13 cm,BC=16 cm ,CD=20cm and DA =5cm.if BD=12cm find the area of the quadrilateral, using herons formula

Answer 1

Add the area of the two triangles

Answer 2

Dear Student,

● Answer -

Area = 245.4 sq.cm

◆ Explaination -

# Given -

Four sides of quadrilateral -

a = AB = 13 cm

b = BC = 16 cm

c = CD = 20 cm

d = DA = 5 cm

# Solution -

Semi-perimeter of quadrilateral is calculated by -

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

s = (13 + 16 + 20 + 5) / 2

s = 27 cm

Area of cyclic quadrilateral is -

Area = √[(s-a)(s-b)(s-c)(s-d)]

Area = √[(27-13)(27-16)(27-10)(27-4)]

Area = √(14 × 11 × 17 × 23)

Area = √60214

Area = 245.4 sq.cm

Hence, area of quadrilateral is 245.4 sq.cm.

Thanks dear.