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# MCQ in Plane Geometry Part 2 | Mathematics Board Exam

This is the Multiple Choice Questions Part 2 of the Series in Plane Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in ME Board Exam Syllabi

• MCQ in Venn Diagram | MCQ in Definition of Plane Geometry | MCQ in Angles | MCQ in Circles | MCQ in Ellipse | MCQ in Polygons | MCQ in Triangles | MCQ in Quadrilaterals | MCQ in Trapezoids and Trapeziums | MCQ in Parallelograms | MCQ in Square and Rectangles | MCQ in Rhomboid and Rhombus

#### Continue Practice Exam Test Questions Part 2 of the Series

Choose the letter of the best answer in each questions.

51. The sides of a right triangle have lengths (a โ b), a, and (a + b). What is the ratio of a to b if a is greater than b and b could not be equal to zero?

A. 1 : 4

B. 3 : 1

C. 1 : 4

D. 4 : 1

Solution:

52. Two sides of a triangle measure 8 cm and 12 cm. find its area if its perimeter is 26 cm.

A. 21.33 sq. m.

B. 32.56 sq. cm.

C. 3.306 sq. in.

D. 32.56 sq. in.

Solution:

53. If three sides of a triangle of an acute triangle is 3 cm, 4 cm, and โxโ cm, what are the possible values of x?

A. 1 < x < 5

B. 0 < x > 5

C. 0 < x < 7

D. 1 < x > 7

Solution:

54. In triangle ABC, AB = 8 m and BC = 20 m. one possible dimension of CA is:

A. 13

B. 7

C. 9

D. 11

Solution:

55. In a triangle BCD, BC = 25 m. and CD = 10 m. The perimeter of the triangle may be.

A. 72 m.

B. 70 m.

C. 69 m.

D. 71 m.

Solution:

56. The sides of a triangle ABC are AB = 25 cm, BC = 39 cm, and AC = 40 cm. Find its area.

A. 486 sq. cm.

B. 846 sq. cm.

C. 648 sq. cm.

D. 468 sq. cm.

Solution:

57. The corresponding sides of two similar triangles are in the ratio 3:2. What is the ratio of their areas?

A. 3

B. 2

C. 9/4

D. 3/2

Solution:

58. Find the area of the triangle whose sides are 12, 16, and 21 units.

A. 95.45 sq. units

B. 102.36 sq. units

C. 87.45 sq. units

D. 82.78 sq. units

Solution:

59. The sides of a right triangle are 8, 15 and 17 units. If each side is doubled, how many square units will be the area of the new triangle?

A. 240

B. 300

C. 320

D. 420

Solution:

60. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitudes, if the areas of the triangle differ by 21 square units.

A. 5 & 11

B. 4 & 10

C. 6 & 12

D. 3 & 9

Solution:

61. A triangular piece of wood having a dimension 130 cm, 180 cm, and 190 cm is to be divided by a line bisecting the longest side drawn from its opposite vertex. The area of the part adjacent to the 180-cm side is:

A. 5126 sq. cm.

B. 5162 sq. cm.

C. 5612 sq. cm.

D. 5216 sq. cm.

Solution:

62. Find EB if the area of the inner triangle is ยผ of the outer triangle.

A. 32.5

B. 55.7

C. 56.2

D. 57.5

Solution:

63. A piece of wire is shaped to enclose a square whose area is 169 cm2. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is:

A. 165 cm2

B. 175 cm2

C. 170 cm2

D. 156 cm2

Solution:

64. The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is 4.5 m. What is the area of the room?

A. 36 sq. m.

B. 27 sq. m.

C. 58 sq. m.

D. 24 sq. m.

Solution:

65. A man measuring a rectangle โxโ meters by โyโ meters, makes each side 15% too small. By how many percent will his estimate for the area be too small?

A. 23.55%

B. 25.67%

C. 27.75%

D. 72.25%

Solution:

66. The length of the side of a square is increased by 100%. Its perimeter is increased by:

A. 25%

B. 100%

C. 200%

D. 300%

Solution:

67. A piece of wire of length 52 cm is cut into two parts. Each part is then bent to form a square. It is found that total area of the two squares is 97 sq. cm. the dimension of the bigger square is:

A. 4

B. 9

C. 3

D. 6

Solution:

68. In the figure shown, ABCD is a square and PDC is an equilateral triangle. Find ัฒ.

A. 5ยฐ

B. 15ยฐ

C. 10ยฐ

D. 25ยฐ

Solution:

69. One side of a parallelogram is 10 m and its diagonals are 16 m and 24 m, respectively. Its area is:

A. 156.8 sq. m.

B. 185.6 sq. m.

C. 158.7 sq. m.

D. 142.3 sq. m.

Solution:

70. If the sides of the parallelogram and an included angle are 6, 10 and 100 degrees respectively, find the length of the shorter diagonal.

A. 10.63

B. 10.37

C. 10.73

D. 10.23

Solution:

71. The area of a rhombus is 132 square cm. if its shorter diagonal is 12 cm, the length of the longer diagonal is:

A. 20 centimeter

B. 21 centimeter

C. 22 centimeter

D. 23 centimeter

Solution:

72. The diagonals of a rhombus are 10 cm. and 8 cm., respectively. Its area is:

A. 10 sq. cm.

B. 50 sq. cm.

C. 60 sq. cm.

D. 40 sq. cm.

Solution:

73. Given a cyclic quadrilateral whose sides are 4 cm, 5 cm, 8 cm, and 11 cm. Its area is:

A. 40.25 sq. cm.

B. 48.65 sq. cm.

C. 50.25 sq. cm.

D. 60.25 sq. cm

Solution:

74. A rectangle ABCD which measure 18 by 24 cm is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

A. 2

B. 7/2

C. 54/2

D. 45/2

Solution:

75. The sides of a quadrilateral are 10m, 8 m, 16 m and 20 m, respectively. Two opposite interior angles have a sum of 225ยฐ. Find the area of the quadrilateral in sq. m.

A. 140.33 sq. cm.

B. 145.33 sq. cm.

C. 150.33 sq. cm.

D. 155.33 sq. cm.

Solution:

76. A trapezoid has an area of 36 m2 and altitude of 2 m. Its two bases in meters have ratio of 4:5, the bases are:

A. 12, 15

B. 7, 11

C. 16, 20

D. 8, 10

Solution:

77. Determine the area of the quadrilateral ABCD shown if OB = 80 cm, OA = 120 cm, OD = 150 cm and ัฒ = 25ยฐ.

A. 2272 sq. cm

B. 7222 sq. cm

C. 2572 sq. cm

D. 2722 sq. cm

Solution:

78. A corner lot of land is 35 m on one street and 25 m on the other street. The angle between the two lines of the street being 82ยฐ. The other to two lines of the lot are respectively perpendicular to the lines of the streets. What is the worth of the lot if its unit price is P2500 per square meter?

A. P1,978,456

B. P1,588,045

C. P2,234,023

D. P1,884,050

Solution:

79. Determine the area of the quadrilateral having (8, -2), (5, 6), (4, 1), and (-7, 4) as consecutive vertices.

A. 22 sq. units

B. 44 sq. units

C. 32 sq. units

D. 48 sq. units

Solution:

80. Find the area of the shaded portion shown if AB is parallel to CD.

A. 16 sq. m.

B. 18 sq. m.

C. 20 sq. m.

D. 22 sq. m.

Solution:

81. The deflection angles of any polygon has a sum of:

A. 360ยฐ

B. 720ยฐ

C. 180ยฐ(n โ 3)

D. 180ยฐ n

Solution:

82. The sum of the interior angles of a dodecagon is:

A. 2160ยฐ

B. 1980ยฐ

C. 1800ยฐ

D. 2520ยฐ

Solution:

83. Each interior angle of a regular polygon is 165ยฐ. How many sides?

A. 23

B. 24

C. 25

D. 26

Solution:

84. The sum of the interior angles of a polygon is 540ยฐ. Find the number of sides.

A. 4

B. 6

C. 7

D. 5

Solution:

85. The sum of the interior angles of a polygon of n sides is 1080ยฐ. Find the value of n.

A. 5

B. 6

C. 7

D. 8

Solution:

86. How many diagonals does a pentedecagon have:

A. 60

B. 70

C. 80

D. 90

Solution:

87. A polygon has 170 diagonals. How many sides does it have?

A. 20

B. 18

C. 25

D. 26

Solution:

88. A regular hexagon with an area of 93.53 square centimeters is inscribed in a circle. The area in the circle not covered by hexagon is:

A. 18.38 cm2

B. 16.72 cm2

C. 19.57 cm2

D. 15.68 cm2

Solution:

89. The area of a regular decagon inscribed in a circle of 15 cm diameter is:

A. 156 sq. cm.

B. 158 sq. cm.

C. 165 sq. cm.

D. 185 sq. cm.

Solution:

90. The sum of the interior angle of polygon is 2,520ยฐ. How many are the sides?

A. 14

B. 15

C. 16

D. 17

Solution:

91. The area of a regular hexagon inscribed in a circle of radius 1 is:

A. 2.698 sq. units

B. 2.598 sq. units

C. 3.698 sq. units

D. 3.598 sq. units

Solution:

92. The corners of a 2-meter square are cut off to form a regular octagon. What is the length of the sides of the resulting octagon?

A. 0.525

B. 0.626

C. 0.727

D. 0.828

Solution:

93. If a regular polygon has 27 diagonals, then it is a:

A. Hexagon

B. Nonagon

C. Pentagon

D. Heptagon

Solution:

94. One side of a regular octagon is 2. Find the area of the region inside the octagon.

A. 19.3 sq. units

B. 13.9 sq. units

C. 21.4 sq. units

D. 31 sq. units

Solution:

95. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon.

A. 228.2 sq. units

B. 288.2 sq. units

C. 282.8 sq. units

D. 238.2 sq. units

Solution:

96. The area of a circle is 89.4 square inches. What is the circumference?

A. 35.33 inches

B. 32.25 inches

C. 33.52 inches

D. 35.55 inches

Solution:

97. A circle whose area is 452 cm square is cut into two segment by a chord whose distance from the center of the circle is 6 cm. Find the area of the larger segment in cm square.

A. 372.5

B. 363.6

C. 368.4

D. 377.6

Solution:

98. A circle is divided into two parts by a chord, 3 cm away from the center. Find the area of the smaller part, in cm square, if the circles has an area of 201 cm square.

A. 51.4

B. 57.8

C. 55.2

D. 53.7

Solution:

99. A quadrilateral ABCD is inscribed in a semi-circle with side AD coinciding with the diameter of the circle. If sides AB, BC, and CD are 8 cm, 10 cm, and 12 cm long, respectively, find the area of the circle.

A. 317 sq. cm.

B. 356 sq. cm.

C. 456 sq. cm.

D. 486 sq. cm.

Solution:

100. A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose length is 1cm more than its width, find the area of the rectangle.

A. 256.25 sq. cm.

B. 323.57 sq. cm.

C. 386.54 sq. cm.

D. 452.24 sq. cm

Solution:

### Online Question and Answer in Plane Geometry Series

Following is the list of practice exam test questions in this brand new series:

MCQ in Plane Geometry
PART 1: MCQ from Number 1 โ 50                             Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                        Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                      Answer key: PART 3

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