find out perimeter and area of the quadrilateral ABCD in which ab is equal to 21 CM angle BAC is equal to 90 degree AC is equal to 20 and CD is equal to 42 and a d is equal to 34 CM
Answers
Step-by-step explanation:
Consider Δ BAC
Using the Pythagoras theorem
BC2=AC2+AB2
By substituting the values
BC2=202+212
On further calculation
BC2=400+441
By addition
BC2=841
By taking out the square root
BC=841
So we get
BC = 29cm
We know that
Perimeter of quadrilateral ABCD = AB + BC + CD + AD
By substituting the values
Perimeter = 21 + 29 + 42 + 34
By addition
Perimeter = 126cm
We know that area of Δ ABC = 21×b×h
It can be written as
Area of Δ ABC = 21×AB×AC
By substituting the values
Area of Δ ABC = 21×21×20
On further calculation
Area of Δ ABC = 210cm2
Consider Δ ACD
We know that AC = 20cm, CD = 42cm and AD = 34cm
It can be written as a = 20cm, b = 42cm and c = 34cm
So we get
s=2a+b+c
s=220+42+34
By division
s=48cm
We know that
Area=s(s−a)(s−b)(s−c)
By substituting the values
Area=48(48−20)(48−42)(48−34
So we get
Area=48×28×6×14
It can be written as
Area=