Find the area of the shaded region in the figure given below.
Answers
Answer:
Consider Δ ABD
Using Pythagoras theorem
AB
2
=AD
2
+BD
2
By substituting the values
AB
2
=12
2
+16
2
On further calculation
AB
2
=144+256
By addition
AB
2
=400
By taking out the square root
AB =
400
So we get
AB = 20cm
We know that the area of Δ ABD =
2
1
×b×h
It can be written as
Area of Δ ABD =
2
1
×AD×BD
By substituting the values
Area of Δ ABD =
2
1
×12×16
On further calculation
Area of Δ ABD = 96cm
2
Consider ΔABC
s=
2
a+b+c
s=
2
20+48+52
By division
s=60cm
We know that
Area=
s(s−a)(s−b)(s−c)
By substituting the values
Area=
60(60−20)(60−48)(60−52)
So we get
Area=
60×40×12×8
It can be written as
Area=
12×5×8×5×12×8
On further calculation
Area=12×5×8
We get
Area=480cm
2
So the area of the shaded region=Area of ΔABC− Area of ΔABD
By substituting values
Area of the shaded region=480−96=384cm
2
Step-by-step explanation:
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