MCQ in Plane Geometry Part 3 | Mathematics Board Exam Practice

Multiple Choice Questions in Plane Geometry Part 3 | Mathematics Board Exam Practice

This is Part 3 of the Plane Geometry MCQ Series on Pinoybix, the final set in this collection and a real test of how far your review has come.

By the time you reach Part 3, you should be moving through plane geometry problems with more confidence and less hesitation than when you started. This set brings together more questions from past board exam problems, engineering mathematics textbooks, academic journals, and other trusted references in the field. These are the kinds of problems that show up in the Mathematics section of the board exam, and working through them carefully gives you a clearer picture of where you actually stand.

At this stage of your review, the goal is not just getting the right answer. It is getting the right answer and being able to explain exactly how you got there. That level of understanding is what holds up when the exam puts a familiar concept in an unfamiliar context, which it will.

Go through every question in this final set with full attention. If something stops you, figure it out. If you get something wrong, understand why before moving on. Part 1 and Part 2 are still available on Pinoybix if you need to revisit anything along the way.

Finish this series strong. The work you put in here is the work that shows up on exam day.

MCQ Topic Outline included in Mathematics 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 3 of the Series

⇐ MCQ in Plane Geometry Part 2 | Mathematics Board Exam

Choose the letter of the best answer in each questions.

101. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

A. 89.5 cm²

B. 58.9 cm²

C. 59.8 cm²

D. 85.9 cm²

102. A sector has a radius of 12 cm. if the length of its arc is 12 cm, its area is:

A. 66 sq. cm.

B. 82 sq. cm.

C. 144 sq. cm.

D. 72 sq. cm.

103. The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector?

A. 4 cm²

B. 9/2 cm²

C. 11/2 cm²

D. 27/2 cm²

104. A swimming pool is to be constructed in the space of partially overlapping identical circles. Each of the circles has a radius of 9 m, and each passes through the center of the other. Find the area of the swimming pool.

A. 302.33 m²

B. 362.55 m²

C. 398.99 m²

D. 409.44 m²

105. Given are two concentric circles with the outer circle having a radius of 10 cm. If the area of the inner circle is half of the outer circle, find the boarder between the two circles.

A. 2.930 cm

B. 2.856 cm

C. 3.265 cm

D. 2.444 cm

106. A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle concentric to this circle and tangent to the given chord.

A. 14π

B. 16π

C. 9π

D. 4π

107. A reversed curve on a railroad track consists of two circular arcs. The central angle of one side is 20° with radius 2500 feet, and the central angle of the other is 25° with radius 3000 feet. Find the total lengths of t he two arcs.

A. 2812 ft.

B. 2218 ft.

C. 2821 ft.

D. 2182 ft.

108. Given a triangle whose sides are 24 cm, 30 cm, and 36 cm. find the radius of a circle which is tangent to the shortest and longest side of the triangle, and whose center lies on the third side.

A. 9.111 cm

B. 11.91 cm

C. 12.31 cm

D. 18 cm

109. Find the area of the largest circle that can be cut from a triangle whose sides are 10 cm, 18 cm, and 20 cm.

A. 11π cm²

B. 12π cm²

C. 14π cm²

D. 15π cm²

110. The diameter of the circle circumscribed about a triangle ABC with sides a, b , c is equal to:

A. a/sin A

B. b/sin B

C. c/sin C

D. all of these

111. The sides of a triangle are 14 cm., 15 cm., and 13 cm. find the area of the circumscribing circle.

A. 207.4 sq. cm.

B. 209.6 sq. cm.

C. 215.4 sq. cm.

D. 220.5 sq. cm.

112. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm?

A. 13.52

B. 14.18

C. 12.73

D. 1564

113. If the radius of the circle is decreased by 20%, by how much is its area decreased?

A. 36%

B. 26%

C. 46%

D. 56%

114. The distance between the center of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. The area of the of the largest circle is:

A. 72π

B. 23π

C. 64π

D. 16π

115. The sides of a cyclic quadrilateral measures 8 cm, 9 cm, 12 cm, and 7 cm, respectively. Find the area of the circumscribing circle.

A. 8.65 cm²

B. 186.23 cm²

C. 6.54 cm²

D. 134.37 cm²

116. The wheel of a car revolves n times, while the car travels x km. the radius of the wheel in meter is:

A. 10,000x/(πn)

B. 500x/(πn)

C. 500,00x/(πn)

D. 5,000x/(πn)

117. If the inside wheels of a car running a circular track are going half as fast as the outside wheel, determine the length of the track, described by the outer wheels, if the wheels are 1.5 m apart.

A. 4π

B. 5π

C. 6π

D. 8π

118. A goat is tied to a corner of a 30 ft. by 35 ft. building. If the rope is 40 ft. long and the goat can reach 1 ft. farther than the rope length, what is the maximum area the goat can cover?

A. 5281 ft²

B. 4084 ft²

C. 3961 ft²

D. 3970 ft²

119. The interior angles of a triangle measures 2x, x + 15, and 2x + 15. What is the value of x?

A. 30°

B. 66°

C. 42°

D. 54°

120. Two complementary angles are in the ratio 2:1. Find the larger angle.

A. 30°

B. 60°

C. 75°

D. 15°

121. Two transmission towers 40 feet high is 200 feet apart. If the lowest point of the cable is 10 feet above the ground, the vertical distance from the roadway to the cable 50 feet from the center is:

A. 17.25 feet

B. 17.5 feet

C. 17.75 feet

D. 18 feet

122. What is the area bounded by the curves y² = 4x and x² = 4y

A. 6.0

B. 7.333

C. 6.666

D. 5.333

123. What is the area between y = 0, y =  3x² , x = 0, and x = 2?

A. 8

B. 12

C. 24

D. 6

124. A circle with radius 7 cm has half its area removed by cutting off a border of uniform width. Find the width of the border. 

A. 2.12 cm

B. 1.98 cm

C. 2.06 cm

D. 2.24 cm

125. The angle of depression from an airplane to the top of an air traffic control tower is 56°. If the tower is 320 feet tall and the airplane is flying at an altitude of 7,450 feet, how far away is the airplane from the control tower?

A. 8,620.27 feet

B. 8,600.72 feet

C. 8,580.93 feet

D. 8,640.15 feet

126. A circle with radius 6 has half its area removed by cutting off a border of uniform width. Find the width of the border.

A. 2.2

B. 1.35

C. 3.75

D. 1.76

127. If the radius of the circle is decreased by 20%, by how much is its area decreased?

A. 46%

B. 36%

C. 56%

D. 26%

128. A 50-meter cable is divided into two parts and formed into two squares. If the sum of the areas is 100 sq. meters, find the difference in length?

A. 21.5

B. 20.5

C. 26.5

D. 0

129. Find the equation of the directrix of the parabola y² = 16x.

A. x = -4

B. x = -8

C. x = 4

D. x = 8

130. A rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of different sides of the square. The ratio of the area of the rectangle to that of the square is _____.

A. 7:72

B. 2:7

C. 4:9

D. 5:9

131. What is the apothem of a rectangular polygon having an area of 225 square units and a perimeter of 60 units?

A. 6.5

B. 7.5

C. 5.5

D. 8.5

132. The sum of the base and the altitude of an isosceles triangle is 36 cm. Find the altitude of the triangle if its area is to be a maximum.

A. 16 cm

B. 17 cm

C. 18 cm

D. 19 cm

133. The measure of each interior angle of a regular polygon is 36 degrees more than its adjacent exterior angle. How many sides have the polygon?

A. 7

B. 6

C. 5

D. 8

134. The midpoint of the sides of a 2 m x 2 m square are interconnected to form a smaller square. The midpoints of the sides of the square formed are again interconnected to form another smaller square. If the process will be repeated indefinitely, find the sum of the areas of all the squares formed including that of the original square.

A. S_∞ = 6 sq. m.

B. S_∞ = 7 sq. m

C. S_∞ = 8 sq. m

D. S_∞ = 5 sq. m

135. Find the area of hex decagon of trimester 32 units.

A. 80.44 sq. units

B. 90.44 sq. units

C. 50.55 sq. units

D. 50.44 sq. units

136. The radius of a circle is diminished by 20%, then its area will be diminished by ______.

A. 46%

B. 36%

C. 26%

D. 16%

137. If the perimeter of a regular octagon is 160, find the length of its apothem.

A. 24.41

B. 21.41

C. 24.14

D. 21.14

138. The hypotenuse of a right triangle is 34 m and one leg is 14 cm longer than the other. The lengths of the two legs are _____ and _____ cm.

A. 12 and 30

B. 14 and 30

C. 16 and 30

D. 16 and 12

139. A pennant in the shape of an isosceles triangle is to be constructed for the Slidell High School Athletic Club and sold at a fund-raiser. The company manufacturing the pennant charges according to perimeter, and the athletic club has determined that a perimeter of 149 centimeters should make a nice profit. If each equal side of the triangle is twice the length of the third side, increased by 12 centimeters, find the lengths of the sides of the triangle pennant.

A. 24, 63, 63

B. 25, 62, 62

C. 26, 61, 61

D. 27, 60, 60

140. A sprinkler that sprays water in a circular pattern is to be used to water a square garden. If the area of the garden is 920 square feet, find the smallest whole number radius that the sprinkler can be adjusted to so that the entire garden is watered.

A. 18 ft.

B. 20 ft.

C. 22 ft.

D. 24 ft.

141. Find the height of the triangle ABC drawn to side BC if AC = 7 , BC = 11 and m∠ACB = 60°.

A. 5√3/2

B. 7√3/2

C. 6√2/2

D. 4√5/2

142. Find the length of the median of a triangle ABC drawn to side BC if AB = 5, AC = 4 and BC = 3.

A. √73/2

B. √75/2

C. √70/2

D. √73/3

143. A triangle has side lengths 5, 6 and 7. How long is the angle bisector drawn to the side of the triangle with length 6?

A. √98/2

B. √105/2

C. √110/2

D. √108/2

144. An engineer was told that a survey had been made on a certain rectangular field but the dimension had been lost. An assistant remembered that if the field had been 100 ft. longer and 25 ft. narrower, the area would have been increased by 2500 sq. ft, and that if it had been 100 ft. shorter 50 ft. wider, the area would have been decreased 5000 sq. ft. What was the area of the field?

A. 25.000 ft²

B. 15,000 ft²

C. 20,000 ft²

D. 22,000 ft²

Online Question and Answer in Plane Geometry Series

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