Question

10. The parallelogram ABCD is inherent in a circle. If AB = 12 cm and AC = 37 cm, find the area of ​​ABCD.​

Answer 1

Step-by-step explanation:

Let O be the intersecting point of AC and BD

We know,

diagonals of a parallelogram bisect each other

OA =OC = 1/2×AC = 10cm

OB = OD= 1/2×BD = 8cm

in ∆AOB

OA=10cm

OB=8cm

AB=12cm

By using Heron's formula

ar(∆AOB)=√s(s-a)(s-b)(s-c)

s=(a+b+c)/2=(12+8+10)/

2=30/2=15cm

ar(∆AOB)=√15×3×7×5

= 15√7 cm²

we know that the diagonals of a parallelogram divides it into four equal triangles

=>ar(∆AOB)=ar(∆BOC)=ar(∆COD)=ar(∆AOD)= 15√7 cm²

ar(ABCD) = 4*15√7 = 60√7 cm² (Ans.)