11. AREAS OF PARALLELOGRAMS AND
TRIANGLES
_______________________________________________________________________________________
TOTAL MARKS : 25
MAXIMUM TIME : 45 Mins.
PART – A
Fill in the blanks by selecting the proper alternative from those given below each question.
(1 mark each)
1. In m ABCD, let
be the altitude corresponding to the base
and
the altitude corresponding
to the base
. If AB = 10 cm, AM = 6 cm and CN = 12 cm, then BC = _____ cm.
(A) 20
2.
and
(A) 12
3.
and
(A) 2.5
4.
(C) 12
(D) 5
are the altitudes of ABC. If AD = 6 cm, BC = 16 cm, BE = 8 cm, then CA = _____ cm.
(B) 18
(C) 24
(D) 12
are the altitudes of ABC. If BE = 10 cm, CA = 8 cm, AB = 16 cm, then CF = _____ cm.
(B) 5
(C) 10
(D) 6.4
ABCD is a rhombus. If AC = 12 cm and BD = 15 cm, then the area of the rhombus ABCD = _____
cm2.
(A) 90
5.
(B) 10
(B) 180
(C) 45
(D) 360
ABCD is a rhombus. If ABCD = 80 cm2 and AC = 8 cm, then BD = _____ cm.
(A) 5
(B) 10
(C) 20
(D) 40
6. In ABC, P, Q and R are the midpoints of
= _____ cm2.
(A) 15
(B) 30
(C) 45
,
and
respectively. If ABC = 60 cm2, then PBCR
(D) 75
7. The union of a triangle and its interior is called _____ .
(A) triangle
(B) interior of triangle
(C) triangular plane
(D) triangular region
8. In ABC, if B – D – C, then area of *ABC = _____ .
(A) area of *ABC + area of *ABC
(C) area of *ADC + area of *ABC
(B) area of *ABD + area of *ADC
(D) area of *ABC – area of *ADC
9. Area of a parallelogram is the product of any of its _____ and its corresponding base.
(A) adjacent side
(B) opposite side
(C) any one side
(D) altitude
10. Two triangles on the same base and lying between pair of parallel lines have same _____ .
(A) perimeter
(B) area
11. In a trapezium ABCD,
ABCD = _____ .
12.
(C) angles
||
(D) volume
(A)
(DM + AB) x CD
(B)
(AD + CD) x AB
(C)
(AB + CD) x DM
(D)
(AB + CD) x DM
and
are altitudes of m DEFG. Their corresponding bases are
= 8, EM = 10, EN = 4, then FG = _____ .
(A) 5
(B) 10
(C) 20
and A – M – B. Then
. M is the foot of perpendicular from D to
and
respectively. If DG
(D) 40
PART B
SECTION A
Solve the following showing calculations (2 marks each)
1. In ABC,
is the altitude to
and
2
ABC = 225 cm , find BF and AE.
2.
is the altitude to
. If AC = 45 cm, BC = 15 cm and
ABC is an equilateral triangle. If BC = 8, find ABC.
3. In a trapezium ABCD,
||
and M and N are the midpoints of
and
respectively.
such that B – E – C. If BC = 16 cm and MN = 10 cm and AE = 6 cm, find ABCD.
4. In a quadrilateral PQRS, m P = 90. Also m SQR = 90. If PS = 9cm, QR = 8 cm and SR = 17 cm,
then find its area.
5. In a trapezium ABCD,
||
. m A = 90,
is altitude to
AM = CM = 24 and BC = 25. Find area of trapezium.
such that A – M – B. CD = 24,
SECTION B
Solve the following showing calculations (3 marks each)
6. Parallelograms having the same base and lying between a pair of parallel lines, have the same area.
Prove it.