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NCERT Class 9 Physics Area of Triangle and Parallelogram Formative Assessment Part 1
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 (1β) 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, 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 and . If AB = 18 cm, AE = 8 cm and CF = 16 cm, find AD.
(a) 9 cm
(b) 8 cm
(c) 10 cm
(d) None of the above
Solution (a)
Parallelogram area = base height
So
Or