# NCERT Class 9 Physics Area of Triangle and Parallelogram Formative Assessment Part 1

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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

a.

b.

c.

d.

e.

f.

g.

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

(a) False. Congruent triangles have equal areas but converse is not true

(b) 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

(C) False. It is corresponding base and corresponding altitude

(d) True.

(e) False. Area is same but perimeter can be different

(f) True

Multiple choice Questions

Question 3

PURS is a rectangle with O as any point in its interior. If area and area, then area of rectangle PQRS

(a) 10

(b) 20

(c) 14

(d) 16

Solution

Answer is (b)

Now PS=QR, So adding

Now

So area of rectangle

Question 4

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

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, ¡t 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 and. If AB = 18cm, AE = 8cm and CF = 16 cm, find AD.

a) 9 cm

b) 8 cm

c) 10cm

d) None of the above

Solution (a)

Parallelogram area= base height

So

Or