Class 9 Maths Question Answers - Areas of Parallelograms and Triangles

 Page 1


                   
 
 
  
       
 
Question:36
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (?ABC) : ar (?BDE).
Solution:
Given:
1 ?ABC is equilateral triangle.
2 ?BDE is equilateral triangle.
3 D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per the instruction given in the question.
We know that area of equilateral triangle = , where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is  cm, Since D is the midpoint of BC.
------
1
------
2
Now, ar(?ABC) : ar(?BDE) = 
Page 2


                   
 
 
  
       
 
Question:36
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (?ABC) : ar (?BDE).
Solution:
Given:
1 ?ABC is equilateral triangle.
2 ?BDE is equilateral triangle.
3 D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per the instruction given in the question.
We know that area of equilateral triangle = , where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is  cm, Since D is the midpoint of BC.
------
1
------
2
Now, ar(?ABC) : ar(?BDE) = 
from1and2
=
Hence we get the result ar(?ABC) : ar(?BDE) = 
Question:37
In the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of rectangle CDEF.
Calculation: We know that,
Area of parallelogram = base × height
The Area of parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Here we can see that rectangle ABCD and Parallelogram CDEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of Rectangle CDEF = 
Question:38
In the given figure, find the area of ?GEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
Page 3


                   
 
 
  
       
 
Question:36
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (?ABC) : ar (?BDE).
Solution:
Given:
1 ?ABC is equilateral triangle.
2 ?BDE is equilateral triangle.
3 D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per the instruction given in the question.
We know that area of equilateral triangle = , where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is  cm, Since D is the midpoint of BC.
------
1
------
2
Now, ar(?ABC) : ar(?BDE) = 
from1and2
=
Hence we get the result ar(?ABC) : ar(?BDE) = 
Question:37
In the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of rectangle CDEF.
Calculation: We know that,
Area of parallelogram = base × height
The Area of parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Here we can see that rectangle ABCD and Parallelogram CDEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of Rectangle CDEF = 
Question:38
In the given figure, find the area of ?GEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of ?GEF.
Calculation: We know that,
Area of Parallelogram = base × height
If a triangle and a parallelogram are on the same base and between the same parallels , the area of the triangle is
equal to half of the parallelogram
Here we can see that Parallelogram ABCD and triangle GEF are between the same base and same parallels.
Hence,
Hence we get the result as 
Question:39
In the given figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of ?EFG.
Solution:
Given:
1 ABCD is a rectangle.
2 AB = 10 cm
3 AD = 5cm
To find: Area of ?EGF.
Calculation: We know that,
Area of Rectangle = base × height
If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is
equal to half of the parallelogram
Page 4


                   
 
 
  
       
 
Question:36
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (?ABC) : ar (?BDE).
Solution:
Given:
1 ?ABC is equilateral triangle.
2 ?BDE is equilateral triangle.
3 D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per the instruction given in the question.
We know that area of equilateral triangle = , where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is  cm, Since D is the midpoint of BC.
------
1
------
2
Now, ar(?ABC) : ar(?BDE) = 
from1and2
=
Hence we get the result ar(?ABC) : ar(?BDE) = 
Question:37
In the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of rectangle CDEF.
Calculation: We know that,
Area of parallelogram = base × height
The Area of parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Here we can see that rectangle ABCD and Parallelogram CDEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of Rectangle CDEF = 
Question:38
In the given figure, find the area of ?GEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of ?GEF.
Calculation: We know that,
Area of Parallelogram = base × height
If a triangle and a parallelogram are on the same base and between the same parallels , the area of the triangle is
equal to half of the parallelogram
Here we can see that Parallelogram ABCD and triangle GEF are between the same base and same parallels.
Hence,
Hence we get the result as 
Question:39
In the given figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of ?EFG.
Solution:
Given:
1 ABCD is a rectangle.
2 AB = 10 cm
3 AD = 5cm
To find: Area of ?EGF.
Calculation: We know that,
Area of Rectangle = base × height
If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is
equal to half of the parallelogram
Here we can see that Rectangle ABCD and triangle GEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of ?GEF = 
Question:40
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find ar
?RAS
Solution:
Given: Here from the given figure we get
1 PQRS is a rectangle inscribed in a quadrant of a circle with radius 10cm,
2 PS = 5cm
3 PR = 13cm
radiusofthequadrant
To find: Area of ?RAS.
Calculation: In right ?PSR,
UsingPythagorasTheorem
Page 5


                   
 
 
  
       
 
Question:36
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (?ABC) : ar (?BDE).
Solution:
Given:
1 ?ABC is equilateral triangle.
2 ?BDE is equilateral triangle.
3 D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per the instruction given in the question.
We know that area of equilateral triangle = , where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is  cm, Since D is the midpoint of BC.
------
1
------
2
Now, ar(?ABC) : ar(?BDE) = 
from1and2
=
Hence we get the result ar(?ABC) : ar(?BDE) = 
Question:37
In the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of rectangle CDEF.
Calculation: We know that,
Area of parallelogram = base × height
The Area of parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Here we can see that rectangle ABCD and Parallelogram CDEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of Rectangle CDEF = 
Question:38
In the given figure, find the area of ?GEF.
Solution:
Given:
1 ABCD is a rectangle.
2 CD = 6 cm
3 AD = 8cm
To find: Area of ?GEF.
Calculation: We know that,
Area of Parallelogram = base × height
If a triangle and a parallelogram are on the same base and between the same parallels , the area of the triangle is
equal to half of the parallelogram
Here we can see that Parallelogram ABCD and triangle GEF are between the same base and same parallels.
Hence,
Hence we get the result as 
Question:39
In the given figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of ?EFG.
Solution:
Given:
1 ABCD is a rectangle.
2 AB = 10 cm
3 AD = 5cm
To find: Area of ?EGF.
Calculation: We know that,
Area of Rectangle = base × height
If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is
equal to half of the parallelogram
Here we can see that Rectangle ABCD and triangle GEF are between the same base and same parallels.
Hence,
Hence we get the result as Area of ?GEF = 
Question:40
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find ar
?RAS
Solution:
Given: Here from the given figure we get
1 PQRS is a rectangle inscribed in a quadrant of a circle with radius 10cm,
2 PS = 5cm
3 PR = 13cm
radiusofthequadrant
To find: Area of ?RAS.
Calculation: In right ?PSR,
UsingPythagorasTheorem
Hence we get the Area of ?RAS = 
Question:41
In square ABCD, P and Q are mid-point of AB and CD respectively. If AB = 8cm and PQ and BD intersect at O, then find
area of ?OPB.
Solution:
Given: Here from the given question we get
1 ABCD is a square,
2 P is the midpoint of AB
3 Q is the midpoint of CD
4 PQ and BD intersect at O.
5 AB = 8cm
To find : Area of ?OPB
Calculation: Since P is the midpoint of AB,
BP = 4cm ……
1
Hence we get the Area of ?OBP =