Geometry

If the length of rectangle A is one-half the length of rectangle B, and the width of rectangle A is one-half the width of rectangle B, what is the ratio of the area of rectangle A to the area of rectangle B?

• ক. 1/4
• খ. 1/2
• গ. 1/1
• ঘ. 2/1

How many times in a day, the hands of a clock are straight?

• ক. 22
• খ. 24
• গ. 44
• ঘ. 48

The angle between the minute hand and the hour hand of the clock when the time is 4.20 is:

• ক. 0°
• খ. 10°
• গ. 5°
• ঘ. 20°

The area of a rectangle is 460 square meters. If the length is 15% more than the breadth, what is the breadth of the rectangular field?

• ক. 15 meters
• খ. 26 meters
• গ. 34.5 meters
• ঘ. None of these

In a garden, there are 10 rows and 12 columns of mango trees. The distance between two trees is 2 meters and a distance of one meter is left from all sides of the boundary of the garden. What is the length of the garden?

• ক. 20 m
• খ. 22 m
• গ. 24 m
• ঘ. 26 m

What is the area of the equilateral triangle if the base BC = 6?

• ক. 9√3
• খ. 18√3
• গ. 26√3
• ঘ. 30√3

If the voluem of a cube is 27 cubic meters, find the surface area of the cube?

• ক. 9 square meters
• খ. 18 square meters
• গ. 54 square meters
• ঘ. 3 square meters

Who is the father of Geometry?

• ক. Aristotle
• খ. Euclid
• গ. Pythagoras
• ঘ. Kepler

If both length and width of a rectangular plot for a garden are increased by 20%, What would be the percent increased in the area of the plot?

• ক. 20%
• খ. 25%
• গ. 35%
• ঘ. 44%

If each angle of a regular polygon is 162°, how many sides does it have?

• ক. 12
• খ. 10
• গ. 8
• ঘ. 16

If the radious of a cylinder is tripled while its height is halved, its volume will be:

• ক. Halved
• খ. Unchanged
• গ. Doubled
• ঘ. Increased by 50%

If the ratio of the radii of the two circles is 3 : 2, than the ratio of the areas of the two circles is:

• ক. 4 : 9
• খ. 9 : 4
• গ. 2 : 3
• ঘ. 3 : 4

The radious of the earth is 4 times that of the moon. How many times the surface area of the moon is to that of the earth?

• ক. 64
• খ. 6
• গ. 36
• ঘ. 32

One angle of triangle is four times the second angle and the third angle is 6 degrees more than the second angle. The second angle in degree is--

• ক. 35
• খ. 40
• গ. 30
• ঘ. 45

To find the diameter of a circle where circumference is 30 inches:

• ক. multiply 30 by π
• খ. divide 30 by 2π
• গ. divide 15 by 2π
• ঘ. divide 30 by π

A painter has painted one-third of a rectangular wal which is ten feet high. When he will paint another 75 sq. feet of that wall, he will have finished three-quarters of the job. What is the length of the wall?

• ক. 10 feet
• খ. 9 feet
• গ. 18 feet
• ঘ. 12 feet

A square water tank 2.5 meter deep, can hold 80.000 liters of water. Find length in meters of each side of the tank.

• ক. 56.57
• খ. 4√2
• গ. 5.25
• ঘ. 5.5

If radious of a circle is increased by 100%, by what % is area of the circle increased?

• ক. 300%
• খ. 200%
• গ. 100%
• ঘ. 500%

A 2 feet wide circular path is created around a circular field with a radious of r feet. Find the value of r, in feet, if the area of the field including the path is twice that of the field alone?

• ক. 2 + 2√2
• খ. 4√2
• গ. 6√2
• ঘ. 2√2

If the length of a rectangular field is 30 feet more than its width and the perimeter is 380 feet, the area of the field is (in sq. feet):

• ক. 11400
• খ. 8800
• গ. 11800
• ঘ. 9400

You need to plant three along the perimeter of a rectangle whose width is 20 ft and length 60 ft. The distence between each plant should be 5 ft. How many trees will you need?

• ক. 33
• খ. 34
• গ. 35
• ঘ. 31

In redesigning a werehous, the lenght is increased by 20%, the breadth is increased by 40% and the heightis decreased by 25%. What is the net increase in the volume of the redesigned werehouse compared to the previous design?

• ক. 40%
• খ. 26%
• গ. 15%
• ঘ. 20%

A farmer has two rectangular fields. The larger field has twice the length and four times the width of the smaller field. If the area of the smaller field is k units, what is the area of the larger field?

• ক. 4k
• খ. 8k
• গ. 10k
• ঘ. 2k

How much will it cost to fence in a field that is 360 vm long and 160 cm wide with fence costs Tk.100 a meter?

• ক. 1060
• খ. 1000
• গ. 1020
• ঘ. 1040

The area of a rectangle is 200 sq. meter. If the length is twice the breadth, what is the perimeter of the rectangle?

• ক. 60
• খ. 30
• গ. 40
• ঘ. 50

From the time 6:15 pm to the time 7:45 pm of the same day, how many degrees does the minute hand of a standrad clock rotate?

• ক. 180
• খ. 190
• গ. 360
• ঘ. 45

If the co-ordinates of A and B are (x, y) and (x, -y) respectively, then the co-ordinates of the midpoint of AB are:

• ক. (x, y)
• খ. (0, y)
• গ. (-x, -y)
• ঘ. (0, 0)

The width of a rectangular fields is 1/3 rd its length. What is the area of the field in square yards if its length is 120 yeards?

• ক. 480
• খ. 5000
• গ. 2400
• ঘ. 4800

A farmer has two rectangular fields. The larger field has twice the length and four times the width of the smaller field. If the area of the smaller field is K units, what is the area of the larger field?

• ক. 2K
• খ. 6K
• গ. 7K
• ঘ. 8K

What is the area of a circle with aradious of 7 meters?

• ক. 154 sq. meters
• খ. 160 sq. meters
• গ. 185 sq. meters
• ঘ. 162 sq. meters

In a right angled triangle the horizontal side measures 8 cm and the verticalside measures 12 cm. What is the area of the triangle?

• ক. 96 sq. cm
• খ. 52 sq.cm
• গ. 48 sq.cm
• ঘ. 100 sq.cm

If the co-ordinates of A and B are (4, 1) and (-2, 7) respectively, then the co-ordinates of the midpoint of AB are:

• ক. (1, 4)
• খ. (-3, 4)
• গ. (3, -4)
• ঘ. (-1, 4)

ABC is a right angle of an isosceles triangle ∆ABC. BD is perpendicular to AC. Which of the following if any is not a 45° angle?

• ক. ∠BAD
• খ. ∠BCD
• গ. ∠CBD
• ঘ. ∠ABD

A circular grass walk of 2 feet wide surrounded a pond of 100 fet in diameter. In terms of π, how many square feet grass walk are there?

• ক. 204 π
• খ. 102 π
• গ. 404 π
• ঘ. 202 π

A circular flower bed has diameter 4m. The flower bed is increased so that the diameter is now 12 m. How many times longer is the new flower bed?

• ক. 9
• খ. 3
• গ. 32
• ঘ. 8

A gerden is 60m long and 20m wide. Inside the garden there is a 5m wide path around it.The area of the path is in square meter.

• ক. 700
• খ. 650
• গ. 375
• ঘ. 500

A line segment is drawn from point (8, -2) to point (4,6). The coordinates of the mid point of this line segment are--

• ক. (12, 4)
• খ. (12, 8)
• গ. (6, 4)
• ঘ. (6,2)

How many spokes are there in a wheel of a car, if any two spokes from an angle of 15°?

• ক. 12
• খ. 15
• গ. 22
• ঘ. 24

The length of a rectangle is increased by 50%, by what percent would the width have to be decreased to maintain same area?

• ক. 33.33
• খ. 50
• গ. 66.67
• ঘ. 150

If 60% of a rectangular floor is covered by a rectangular rug of 9 feet by 12 feet, what is the area in square feet of the floor?

• ক. 65
• খ. 108
• গ. 180
• ঘ. 270

In the figure below, AB is perpendicular to BC and DB = DC. If AD = √10 cm and AC = 4 cm, what is the value of BC?

• ক. 5cm
• খ. 4 cm
• গ. 8 cm
• ঘ. 10 cm

A rectangular carpet, that is 9 feet by 12 feet, covers 60% of a rectangular floor. What is the area of the floor?

• ক. 300 square feet
• খ. 180 square feet
• গ. 108 square feet
• ঘ. 64.8 square feet

Starting from Town S, Mr. Ahsan drove straight East for 3 kms, then he turned left and drove straight North for 4 kms and stopped at Town T. What is the straight-line distance from Town S to Town T?

• ক. √7 kms
• খ. 5 kms
• গ. 8 kms
• ঘ. 2√3 kms

If a square region (PQRS) has an area of 4 square feet, what is the length of its diagonal(PR)?

• ক. 4 feet
• খ. 2 feet
• গ. 8 feet
• ঘ. 2√2 feet

What is the width of a rectangular field, whose length is 70 feet more than its width and the perimeter is 500 feet?

• ক. 60 feet
• খ. 70 feet
• গ. 80 feet
• ঘ. 90 feet

If the area of a circle is 25π then diameter of the circle is--

• ক. 6
• খ. 10
• গ. 20
• ঘ. 25

In square ABCD below, if DE = EB and DF = FC, then the area of the shaded region is what fraction of the area of square region ABCD?

• ক. 1/16
• খ. 1/8
• গ. 1/4
• ঘ. 1/6

ABCD is a square, EFGH is arectangle, AB = 3, EF = 4, FG = 6. Determine the area of the region outside of ABCD and inside of EFGH.

• ক. 24
• খ. 9
• গ. 18
• ঘ. 15

If the coordinates of A and B are (4, 1) and (-2, 7) respectively, then the coordinates of the midpoint of AB are--

• ক. (1, 4)
• খ. (-3, 4)
• গ. (3, -4)
• ঘ. None of these

The diameter of a wheel is 63 cm. Distance traveled by the wheel in 100 revolutions is--

• ক. 99 meters
• খ. 198 meters
• গ. 63 meters
• ঘ. 136 meters

One side of a rectangular field is 4 meters and its diagonal is 5 meters. The area of the field is--

• ক. 12 sq. m
• খ. 15 sq. m
• গ. 20 sq. m
• ঘ. 4√5 sq. m

If the circumference of a circle is increased by 50%, its area will be increased by:

• ক. 50%
• খ. 100%
• গ. 125%
• ঘ. 225%

If a triangle has base B and the altitude of the triangle is twice the base, then the area of the triangle is:

• ক. 1/2AB
• খ. AB
• গ. 1/2B2
• ঘ. B2

A triangle has a base x and and an altitude y. A second triangle has a base twice the altitude of the first triangle and and an altitude twice the base of the first triangle. What is the area of the second triangle?

• ক. 2xy
• খ. 0.5xy
• গ. 0.66 xy
• ঘ. 4xy

How many tiles each 1 foot square are necessary to form a 1 foot border around the inside of a room 24 feet by 14 feet?

• ক. 36
• খ. 37
• গ. 72
• ঘ. 74

What is the area of a square (in sq. meter) if its perimeter is 40 meter?

• ক. 10
• খ. 100
• গ. 200
• ঘ. None of these

The second angle of a right triangle is 30°. Then what is the third angle?

• ক. 50°
• খ. 60°
• গ. 70°
• ঘ. 80°

The perimeter of rectangle is 200 meter. The breadth is 3/7 part of the length. What is the length?

• ক. 30m
• খ. 50m
• গ. 60m
• ঘ. 70m

A circle wheel 28 inches in diameter rotates the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minute does the larger wheel make in terms of x?

• ক. 12x
• খ. 48x
• গ. 24x
• ঘ. 36x

If two sides of the triangle below have lengths 5 and 6, the perimeterof the triangle could be which of the following? I. 11 II. 15 III.24

• ক. I only
• খ. II only
• গ. III only
• ঘ. II and III only

If the length and width of a ractangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

• ক. 44%
• খ. 24%
• গ. 36%
• ঘ. 40%

A rectangle area of 16 meters by 12 meters. is surrounded by a road of 3 meters wide. The area of the road is:

• ক. 78
• খ. 132
• গ. 204
• ঘ. 216

If the legs of a right triangle is 3 and 4, then the length of hypotenuse is approximately:

• ক. 3
• খ. 4
• গ. 5
• ঘ. 6

If an angle of a parallelogram is 60 degrees, find the number of degree of remaining angles.

• ক. 60, 60, 60
• খ. 30, 60, 90
• গ. 60, 120, 120
• ঘ. 60, 120, 150

The area of a rectangular R width 4 feet is equal to the area of a square S which has a perimeter of 24 feet. The perimeter of the rectangular R, in feet is--

• ক. 9
• খ. 16
• গ. 24
• ঘ. 26

Find the volume of a triangular solid cylinder with the following dimensions: 4 feet base, 3 feet height of the triangle and 10 feet height of the cylinder?

• ক. 120 cft
• খ. 60 cft
• গ. 80 cft
• ঘ. 65 cft

How many rectanggular are there in the following figure:

• ক. 6
• খ. 8
• গ. 9
• ঘ. 10

The floor of a company's office has an area of 20000 square feet. If the floor is in the shape of a square approxmately how many feet long is each side?

• ক. 140
• খ. 450
• গ. 500
• ঘ. 1000

Saurabh has purchased a square sheet of plywood 196 square feet area. To cover a wall he must cut off 3 feet from a side. What is the area in square feet of the wall?

• ক. 154
• খ. 144
• গ. 169
• ঘ. 168

A carpet that measures 6 ft by 8 ft covers 60% of a floor. What is the area of the floor?

• ক. 60
• খ. 100
• গ. 80
• ঘ. 90

The length of a rectangle is 1 inch more than 2 times its width. The area of the reatangle is 36 square inches. What is the length of the rectangle?

• ক. 4 inches
• খ. 6 inches
• গ. 9 inches
• ঘ. 18 inches

Triangle XYZ and two angles measure are shown in the diagram below. What is the measure of ∠Y?

• ক. 50°
• খ. 85°
• গ. 90°
• ঘ. 95°

In the figure below ∠R and ∠S are formed by two inteesecting lines. If ∠R measures 53°, what is the measure of ∠S?

• ক. 35°
• খ. 55°
• গ. 110°
• ঘ. 125°

A rectangular tank 10 inch by 8 inch by 4 inch is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?

• ক. 9
• খ. 12
• গ. 16
• ঘ. 21

If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?

• ক. 50%
• খ. 100%
• গ. 200%
• ঘ. 300%

Ashraful has purchased a square sheet of plywood 169 square feet area. To cover a wall he must cut off 3 feet from a side. What is the area in square feet of the wall?

• ক. 154
• খ. 144
• গ. 196
• ঘ. 130

A carpet that measures 5 ft by 9 ft covers 75% of a floor. What is the area of the floor?

• ক. 60
• খ. 100
• গ. 80
• ঘ. 90

How many tiles each a square tile of 2 inch sides are needed to cover a rectangle floor of 4 feet long and 6 feet wide?

• ক. 24
• খ. 128
• গ. 96
• ঘ. 864

A farmer has two rectangular fields. The larger field has twice the length and four times the width of the smaller field. If the smaller field has area k, then the area of the larger field is greater than the area of the smaller field by what amount?

• ক. 2k
• খ. 6k
• গ. 7k
• ঘ. 8k

Shahin has purchased a square sheet of plywood of 169 square feet area. To cover a wall he must cut off two feet from a side. What is the area, in square feet of the wall?

• ক. 117
• খ. 121
• গ. 143
• ঘ. 141

In the figure below, the area of square PQRS is 64. What is the area of triangle QRT?

• ক. 48
• খ. 32
• গ. 24
• ঘ. 16

If a square is inscribed in a circle of radius r as shown below, then the area of the square region is--

• ক. r2/2∏
• খ. ∏r2/2
• গ. ∏r2
• ঘ. 2r2

Is square ABCD below, what is the value of {(AC)(AD)}/{(AB)(DC)} =?

• ক. 1/2
• খ. 1
• গ. √2
• ঘ. 2

If P is the center of the circle, then what fraction of the circle region is shaded?

• ক. 1/12
• খ. 1/9
• গ. 1/6
• ঘ. 1/5

Given AB = 4 & AC = 5, the perimeter of the ractangle is--

• ক. 18
• খ. 40
• গ. 14
• ঘ. 22

The length of sides AB and AC in the triangle below are equal. What is the measure of angle A?

• ক. 70°
• খ. 55°
• গ. 40°
• ঘ. 110°

If four triangles are constructed with sides of the length indicated below, which of the following triangles will not be a right triangle?

• ক. 5, 12, 13
• খ. 8, 15, 17
• গ. 12, 15, 18
• ঘ. 3 , 4, 5

The sum of the angles of a square is:

• ক. 90°
• খ. 180°
• গ. 360°
• ঘ. 200°

What is the volume of a cube that has a total surface area of 54?

• ক. 9
• খ. 27
• গ. 54
• ঘ. 81

The length of a rectangular floor is one and a half times its breadth. What is the perimeter of the floor (in meters) if its area is 216 sq. meters:

• ক. 40
• খ. 50
• গ. 60
• ঘ. 44