From the given data find perimeter of □ABCD, AD = 6 √2 cm. * From the given data find perimeter of □ABCD, AD = 6 √2 cm. *
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Answers
Answer:
perimeter of the square =4a
=4×6√2
=24√2
Step-by-step explanation:
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Answer:
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=16×3×14×2×3×2×14
On further calculation
Area=4×3×14×2
By multiplication
Area=336cm2
So the area of quadrilateral ABCD =Area of ΔABC+ Area of ΔACD
By substituting the values
Area of the quadrilateral ABCD=210+336=546cm2
Therefore, the perimeter is 210cm and the area is $$546cm^2