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Mathematics Lesson 4: Geometry Review
8-AOS AET
___/___/_____
65 Questions in 80 Minutes
First 15 questions work in class.
Full set (first 15 PLUS the next 50 questions) : Homework
Student’s Name:____________________________
1.
Score:_________________________
ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then A and B , respectively
are ___.
A) 600,1200
2.
3.
B) 1200,600
C) 800,1000
D) 1000,800
The sum of the measures of the internal angles of any polygon is ___.
A) 1800
B) 3600
C) 5400
D)depends on the number of sides
ABCD is a quadrilateral. If AC and BD bisect each other, then ABCD must be ___.
A) Square
B) Rectangle
C) Parallelogram
D) Rhombus
4.
ABCD is a quadrilateral. If AC and BD bisect each other at right angles, then ABCD must be ___.
A) Square
B) Rectangle
C) Parallelogram
D) Rhombus
5.
The number of sides of a regular polygon whose each interior angle has a measure of 144 0 is ___.
A) 4
6.
B) 6
B) 900
C) Depends on the angles A and D
C) D
D) 900
B) Trapezium
C) Parallelogram
D) None of these
In a parallelogram ABCD, if A = 450, then the other angles are ___.
A) 450,1200,1200
10.
B) A
If there are two pairs of opposite sides of a quadrilateral which are equal and parallel, it is ___.
A) Kite
9.
D) Not able to determine from given data
If ABCD is an isosceles trapezium, C is equal to _____.
A) B
8.
D) 10
ABCD is a parallelogram. The angle bisectors of A and D meet at O. The measure of AOD is ____.
A) 450
7.
C) 8
B) 450,1350,1350
C) 600, 1350,1350
D) 600,1200,1200
ABCD is rhombus. If ACB = 400, then ADB is ____.
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A) 450
11.
B) 400
D) 1200
The sum of the internal angles of quadrilateral is ___.
A) 1800
12.
C) 500
B) 3600
C) 2700
D) Depending on the type of quadrilateral
In the given figure, line RT is drawn parallel to SQ.
If QPS = 100 , PQS = 40 ,
0
0
PSR = 850 and
QRS = 700 , then QRT is ___.
A) 450
13.
B) 650
C) 850
D) 900
Choose the correct statement.
A) The diagonals of a parallelogram are equal.
B) The diagonals of a rectangle are perpendicular to each other.
C) If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.
D) Every quadrilateral is either a trapezium or a parallelogram or a kite.
14.
Four angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. The greatest angle is __.
A) 1250
15.
C) 1350
D) 1200
C) Right angle
D)
Diagonals of a rhombus bisect each other at __.
A) Acute angle
16.
B) 750
B) Obtuse angle
1
right angle
2
ABCD is a parallelogram as shown. Then the angles x and y are related as __.
A) x = y
B) x < y
C) x > y
D) Cannot be determined from given data
17.
Which of the following statements is true ?
A) The diagonals of a rectangle are perpendicular
B) The diagonals of a rhombus are equal
C) Every square is a rhombus
D) Every rhombus is a square
18. ABCD is a quadrilateral. AB = BC=CD=DA and
A = B = C = D = 900 . Then ABCD can be called
___.
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A) Rhombus
B) Square
C) Parallelogram
D) Trapezium
19. Which of the following statements is not true in case of a rectangle ?
A) It has two pair of equal sides
B) It has all its sides of equal length
C) Its diagonals are equal
D) Its diagonals bisect each other
20. In the given figure, P is a point in the interior of AOB and AOB = 360.
If PM ⊥ OA and PN ⊥ OB. Then x is ___.
A) 1440
21.
D) 450
B) 720, 360
C) 1000,800
D) 1440,360
If ABCD is a parallelogram, then A − C is _____.
A) 1800
23.
C) 2160
If two adjacent angles of a parallelogram are in the ratio 3 : 2, then the measure of the angles are ___.
A) 1080, 720
22.
B) 900
B) 00
C) 3600
D) 900
In the given quadrilateral EFGH, HG=HE=HF; If the internal angle F = 60º, what is the sum of the internal
angles G+E ?
A) 30º
B) 45º
C) 60º
D) Can’t be determined
24.
The diagonals of a parallelogram ABCD intersect at O. If
BOC = 900 and BDC = 500 , then
AOB is ___.
A) 100
25.
B) 400
C) 500
D) 900
The ratio of sides of a parallelogram is 3 : 5 and the perimeter is 48 in, then the sides of the parallelogram are
___.
A) 9 in, 12 in
26.
B) 9 in, 15 in
C) 10 in, 12 in
D) 8 in, 15 in
One of the diagonals of a rhombus is equal to a side of the rhombus. The internal angles of the rhombus are
two pairs of ____.
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A) 600 and 800
27.
ABCD is a parallelogram. AC ⊥ BD and
C) 1200 and 2400
D) 1000 and 1200
ACD = 300 , then ABD is ___.
B) 600
A)
28.
B) 600 and 1200
C) 900
D) 1200
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD
is a ____.
A) Square
29.
B) Parallelogram
C) Rhombus
D) Trapezium
If the lengths of two diagonals of a rhombus are 12in and 16in, then the length of each side of the rhombus is
___.
A) 10 in
30.
C) Not possible to determine D) 5in
PQRS is a rhombus. The value of perimeter if PR = 10 in and QS = 24 in is ___.
A) 50 in
31.
B) 14 in
B) 51 in
C) 52 in
D) 53 in
The given figure HOPE is a parallelogram. The relation between x,y and z is ____.
A) x = y + z
B) y + z – x = 1800
C) x + y – z = 1800
D) x + y = 1800 - z
32.
The diagonals of a rhombus are 7.5 in and 12 in. Then the area of rhombus is …..
A) 45 in2
33.
C) 22.5 in2
D) 180 in2
The ratio of areas of two squares, one having double its diagonal than the other, is…..
A) 3 : 2
34.
B) 90 in2
B) 4 : 1
C) 3 : 1
D) 4 : 3
What change in percent is made in the area of a rectangle by decreasing its length by 10% and increasing its
breadth by 10% ?
A) No change
35.
A) 4
38.
D) 1 % increase
B) 30 ft
C) 100 ft
D) 6o ft
The length of the longest rod that can fit in a cubical room of 4 m side is ……
A) 8.66 m
37.
C) 1 % decrease
A person walked 50 ft. to cross a rectangular field diagonally. If the width of field is 30 ft, its length is …..
A) 40 ft
36.
B) 5 % increase
B) 5.196 m
C) 6.928 m
D) 5 m
The area of a rhombus is 28 in2 and one of its diagonals is 4 in. Its perimeter is …..
53 in
B) 36 in
C) 2
53 in
D) None of these
The adjacent sides of a parallelogram are 8 in and 9 in. The diagonal joining the ends of these sides is 13 in.
Its area is …..
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A) 72 in2
39.
B) 12 35 in2
C) 24 35 in2
D) 150 in2
A square garden measuring 8 m on a side is surrounded by a 1 m wide path. What is the area of the pathway?
A) 8 sq. m
B) 9 sq. m
C) 16 sq. m
D) 36 sq. m
40.
In the given figure, LMNO and GHJK are rectangles where GH =
1
1
LM and HJ =
MN. What fraction of
2
2
the region is bounded by LMNO that is not shaded ? ( Figure not drawn to scale)
A)
41.
1
4
B)
C)
1
2
D)
3
4
Each side of a cube is increased by 50%. Then the surface area of the cube increases by ……..
A) 50 %
42.
1
3
B) 100 %
C) 125 %
D) 150 %
In the given figure, RSTV is a square inscribed in a circle with center O and radius r. The total area of shaded
region is ……( Figure not drawn to scale)
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A) r2
43.
(  − 2)
A)
45.
(2 − )
C)

(r2 - 2)
D) 8r2 – 8r
The length of diagonal of a square whose area is 169 m 2, is…..
A) 13 m
44.
B) 2r2
B) 13
2 m
C) 16.9 m
D) 14.4 m
Two cylinders of same volume have their heights in the ratio 1 : 3. Then the ratio of their radii is ….
3 :1
B)
2 :1
C)
5 : 2
D) 2 :
5
The area of a trapezium is 28 in2 and one of its parallel sides is 6 in. If its altitude is
4 in, then its other
parallel side is ….
A) 8 in
46.
A)
47.
C) 6 in
D) 9 in
If the area of a triangle with base x is equal to area of a square of side x, the altitude of the triangle is …..
x
B) x
2
C)
2 x
D) 2x
The ratio of the areas of a square to that of a square drawn on its diagonal is ……
A) 1 : 1
48.
B) 4 in
B) 1 : 2
C) 1 : 3
D) 1 : 4
A man bought a rectangle plot of 144 m length and 64 m width. In exchange for this field he wanted to buy a
square field of the same area. Then the side of the square field would be
A) 104 m
49.
B) 208 m
C) 96 m
D) 406 m
Three cubes whose edges are 3 in, 4 in and 5 in respectively are melted without any loss of metal into a single
cube. The edge of new cube is …..
A) 6 in
50.
B) 12 in
C) 9 in
D) 10 in
Four circles of equal radii are centered at the four vertices of a square. These 4 circles touch a fifth circle of
equal radius placed inside this square. The ratio of the shaded area of the circles to the un-shaded area of the
circles is….
A) 5 : 2
51.
The ratio of radii of two cylinders is 1 :
A) 1 : 9
52.
B) 2 : 9
C) 3 : 2
D) 2 : 5
3 and heights are in the ratio 2 : 3. The ratio of their volume is …..
C) 4 : 9
D) 5 : 9
Two cubes have volume in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is….
A) 1 : 3
53.
B) 2 : 3
B) 1 : 6
C) 1 : 9
D) 1 : 18
Two cubes have volume in the ratio 1 : 27. The ratio of the sides of the cubes is
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A) 1 : 3
54.
A)
B) 1 : 6
C) 1 : 9
D) 1 : 18
What is the ratio of the perimeter of the shaded region to the circumference of the circle
3
4+
B)
4
4
55.
2
4+
D)
4+
2
The volume of a cube is 512 in3. Its surface area is….
A) 64 in2
56.
C)
B) 256 in2
C) 384 in2
D) 512 in2
A quadrilateral whose one diagonal is 5.5 in. If the length of altitudes from opposite vertices on the diagonal
is 2.5 in and 1.5 in, then the area of quadrilateral is ……
A) 22 in2
57.
C) 55 in2
D) 33 in2
C) 6.75 cm2
D) 9 cm2
The surface area of the given cube, is …..
A) 3.375 cm2
58.
B) 11 in2
B) 13.5 cm2
The perimeter of a trapezium is 52 in and its non parallel sides are each equal to 10 in and its altitude is 8 in.
Its area is ….
A) 128 in2
59.
A) 2
61.
C) 118 in2
D) 124 in2
How many small cubes with edges of 10 in can be just accommodated in a cubical box of 100 in edge ?
A) 10 B) 100
60.
B) 112 in2
C) 1000
D) 10000
The largest possible square is inscribed in circle of unit radius. The area of the square in square units is ……
B)

C) 2
2
D) 4
2
The given figure shows a square inscribed in a larger square. What is the area of the smaller square ?
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A) 9 square units
62.
B) 2 : 1
C) 1 :
2
D)
2 :1
B) 1/3 times
C) 1/4 times
D) 1/6 times
The area of the trapezium ABCD as shown in the figure (in square units) is
A) 222
65.
D) 36 square units
If the side of a square is halved, the area of the square becomes
A) 1/2 times
64.
C) 25 square units
Two circular cylinders of equal volume have heights in the ratio of 1 : 2. The ratio of their radii is….
A) 1 : 2
63.
B) 16 square units
B) 111
C) 224
D) 116
The hypotenuse of a right triangle is 29 in and one of its sides is 20 in, then the other side is ……
A) 20 in
B) 21 in
C) 27 in
D) 25 in
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