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Class 9 Maths Important Questions for Area of parallelograms



Given below is Area of parallelogram worksheet

a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's

Question 1

Which of the following figures lie on the same base and between the same parallels?

In such a case, write the common base and the two parallel

Area of parallelogram worksheet

Area of parallelogram worksheet

Solution 1

a) True.  With Base BC and between parallel AD and BC, Triangle QBC and parallelogram ABCD

b) True. With base DC or AB and between parallel DC and AB, triangles are present

c) True. Same as above

d) False

e) True. Same as a

f) False

g) True

 

Question 2

True or False statement

(a) If two triangles area are same areas, they will be congruent

(b) Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

(c) The area of a triangle is equal to the product of any of its side and any altitude

(d) The median of the triangles divides the triangle into two triangles of equal areas

(e) Parallelograms on the same base and between same parallels have same perimeter

(f) In a parallelogram, diagonals divide the parallelogram into four equal triangles

 

Solution

  1. False. Congruent triangles have equal areas but converse is not true
  2. True.  Triangle area is (1/) X base X height. With same base and area, height should be equivalent, which means they lie on same parallel
  3. False. It is corresponding base and corresponding altitude
  4. True. 
  5. False. Area is same but perimeter can be different
  6. True

Multiple choice Questions

 

Question 3

PQRS   is a rectangle with O as any point in its interior. If area (ΔPOS)= 4 cm2 and area(ΔQOR)= 6 cm2, then area of rectangle PQRS

(a) 10cm2

(b) 20cm2

(c) 14 cm2

(d)  cm2

 

Solution

Answer is (b)

$\frac{1}{2}PS \times (alitude)_{1}=4cm^{2}$

$\frac{1}{2}QR \times (alitude)_{2}=6cm^{2}$

Now PS=QR, So adding

$\frac{1}{2}PS \times [(alitude)_{1}+(altitude)_{2}]=10cm^{2}$

Now altitude1 + altitude2= PQ=RS

So area of rectangle=20 cm2

 

Question 4

In the below figure AD is the median, And E is any point on AD

Area of parallelogram worksheet

Which of the following is true?

a) Area of triangle AEB= Area of triangle AEC

b) Area of triangle DEB= Area of triangle DEC

c)  Area of triangle ABD= Area of triangle ADC

d) All the above

Solution (d)

Since AD is median, it bisect the triangle is equal areas

So Area of triangle ABD= Area of triangle ADC    ---(1)

 

Now ED is the median for EBC triangle

So Area of triangle DEB= Area of triangle DEC   --(2)

Subtracting 1 and 2, we get

Area of triangle AEB= Area of triangle AEC

Question 5

In the given figure ABCD is a parallelogram   AE ⊥ DC and   CF ⊥ AD. If AB = 18 cm, AE = 8 cm and CF = 16 cm, find AD.

Area of parallelogram worksheet

a) 9 cm

b) 8 cm

c) 10 cm

d) None of the above

 

Solution (a)

Parallelogram area= base X height

So DC×AE=AD×CF

Or AD=DC×AE/CF=9 cm

 

Question 6

In the below figure AD is the median, and E is mid-point on AD. If the area of triangle is 16 cm2, what is the area of the triangle BED

Area of parallelogram worksheet

(a)  3cm2

(b) 4cm2

(c) 5 cm2

(d) None of these

 

Solution b

Question 7

PQRS is a quadrilateral whose diagonal bisect each other at right angles

a) PQRS is a Square

b) PQRS is a rectangle

c) PQRS is a rhombus

d) None of these

Solution (c)

 

Question 8

In a quadrilateral ABCD, diagonal BD and AC intersect at point X

Area of parallelogram worksheet

Which of the following is true?

(a) (Area of triangle BXC)×( Area of triangle AXD)=( Area of triangle AXB)×(Area of triangle CXD)

(b) (Area of triangle BXC)+( Area of triangle AXD)=( Area of triangle AXB)+(Area of triangle        CXD)

(c) Insufficient information

(d) None of these

Solution (a)

Hint, Draw perpendicular from A and C on BD and the calculate the area of each these piece and arranged them to get the solution

 

Question 9

Two parallelograms are on the same base and between the same parellels. The ratio of their areas is:

a) 1:2

b) 1:1

c) 1:4

d) None of these

 

Solution (b)

Question 10

In a triangle A,B,C,D and E are such point BD=DE=EC

Area of parallelogram worksheet

Which of the following is true?

a) Area of triangle ABD=Area of triangle ADE=Area of triangle AEC

b) Area of triangle ADE=(1/3) Area of triangle ABC

c) Triangle ABD is congruent to triangle AEC

d) None of the above

 

Solution (a), (b)

Hint: Draw perpendicular from A on BC and then calculate area for each of these triangle and you will find it same

 

 

 

 

Match the column

Area of the triangle is 20 cm2, Area of rectangle is

25cm2.

Area of the parallelogram is 100 cm2. Both the Diagonal are drawn which cut the area into four pieces. The area of each piece is

40cm2

 

In a triangle ABC,all the median intersect at point G, If the area of the triangle is 150 cm2,what is the area of the triangle AGC

10 cm2

A trapezoid as parallel sides of 4 and 6 cm respectively, The altitude is 5 cm.A diagonal is drawn which cut the trapezoid into two traingles.Area of the triangle with base 4 cm is

 

 

50 cm2

 

Solution

a) 40 cm2

b) 25cm2

c) 50 cm2

d) 10 cm2