MCQ in Plane Geometry Part 1 | Mathematics Board Exam Practice

Multiple Choice Questions in Plane Geometry Part 1 | Mathematics Board Exam Practice

Plane geometry is one of those foundational topics that shows up in the Mathematics section of the board exam more often than most reviewees expect. Angles, lines, triangles, circles, polygons and the problems look familiar until they are not, and that false sense of comfort is exactly what trips people up.

This is Part 1 of the Plane Geometry MCQ Series on Pinoybix, put together to help engineering students and board exam reviewees build real familiarity with this topic through consistent practice. Every question here was compiled from past board exam problems, engineering mathematics textbooks, academic journals, and other references that have proven useful to reviewees over the years.

Take each question seriously. Plane geometry problems on the board exam are not always as simple as they appear at first glance. Some require careful reading, others require you to draw out the figure before the solution becomes clear. Speed matters on exam day, but understanding comes first.

If this is the start of your review on this topic, you are in the right place. Work through every item, take note of what gives you trouble, and use every wrong answer as a reason to go deeper into the concept. That approach will serve you far better than just checking answers and moving on.

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

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each question.

Problem 1: ECE Board November 1998

Find the angle in mills subtended by a line 10 yards long at a distance of 5000 yards.

A. 1

B. 2

C. 2.5

D. 4

Problem 2: ECE Board April 1999

Assuming that the earth is sphere whose radius is 6400 km. Find the distance along a 3 degree arc at the equator of the earth’s surface.

A. 335.10 km

B. 533.10 km

C. 353.10 km

D. 353.01 km

Problem 3: EE Board April 1992

The angle subtended by an arc is 24°. If the radius of the circle is 45 cm, find the length of arc.

A. 16.85 cm

B. 17.85 cm

C. 18.85 cm

D. 19.85 cm

Problem 4: ME Board April 1990

A rat fell on a bucket of a water wheel with a diameter of 600 cm which travelled at an angle of 190° before it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell.

A. 950

B. 965

C. 985

D. 995

Problem 5: ECE Board November 1992

Given a circle whose diameter AB equals 2 m. if two points C and D lie on the circle and angles ABC and BAD are 18° and 36° respectively, find the length of the major arc CD.

A. 1.26 m

B. 1.36 m

C. 1.63 m

D. 1.45 m

Problem 6:

A certain angle has as supplement 5 times its complement. What is the angle?

A. 67.5°

B. 58.5°

C. 30°

D. 27°

Problem 7: ECE Board November 1998

Each angle of a regular dodecagon is equal to

A. 135°

B. 150°

C. 125°

D. 105°

Problem 8: CE Board May 1997

How many sides has a polygon if the sum of the interior angles is 1080°?

A. 5

B. 6

C. 7

D. 8

Problem 9: ECE Board March 1996

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

A. 3

B. 4

C. 5

D. 6

Problem 10: ECE Board April 1991

Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle.

A. 150°

B. 160°

C. 170°

D. 180°

Problem 11: ME Board April 1999

How many sides are in a polygon if each interior angle is 165 degrees.

A. 12

B. 24

C. 20

D. 48

Problem 12:

How many diagonals are there in a polygon of 20 sides?

A. 200

B. 170

C. 100

D. 158

Problem 13: ME Board April 1999

Find each interior angle of a hexagon.

A. 90°

B. 120°

C. 150°

D. 180°

Problem 14: EE Board April 1994

Given a triangle, C = 100°, A = 15 m, B = 20 m. Find c.

A. 26 m

B. 27 m

C. 28 m

D. 29 m

Problem 15: CE Board November 1994

In triangle ABC, angle A = 45° and C = 70°. The side opposite angle C is 40 m long. What is the length of the side opposite angle A?

A. 26.1 m

B. 27.1 m

C. 29.1 m

D. 30.1 m

Problem 16: CE Board May 1995

In triangle ABC, angle C = 70°, A= 45°, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

A. 36.3 m

B. 36.6 m

C. 36.9 m

D. 37.2 m

Problem 17: EE Board April 1991

From a point outside of an equilateral triangle, the distances to the vertices are 10 m, 18 m and 10 m, respectively. What is the length of one side of a triangle?

A. 17.75 m

B. 18.50 m

C. 19.95 m

D. 20.50 m

Problem 18: EE Board April 1991

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed circle.

A. 2.25 cm

B. 2.35 cm

C. 2.45 cm

D. 2.55 cm

Problem 19: CE Board May 1996

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

A. 12.73 m

B. 13.52 m

C. 14.18 m

D. 15.55 m

Problem 20: EE Board April 1991

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the circumscribing circle.

A. 7.14 cm

B. 7.34 cm

C. 7.54 cm

D. 7.74 cm

Problem 21: CE Board May 1996

Two sides of a triangle are 50 m and 60 m long. The angle included between these sides is 30°. What is the interior angle opposite the longest side?

A. 93.74°

B. 92.74°

C. 90.74°

D. 86.38°

Problem 22: ECE Board March 1996

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

A. 1.76 cm

B. 1.35 cm

C. 1.98 cm

D. 2.03 cm

Problem 23: ME Board April 1996

The area of a circle is 89.42 sq. inches. What is its circumference?

A. 32.25 in.

B. 33.52 in.

C. 35.33 in.

D. 35.55 in.

Problem 24: ECE Board April 1991

A square section ABCD has one of its sides equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED.

A. 130°

B. 140°

C. 150°

D. 160°

Problem 25: CE Board November 1995

The area of a circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m?

A. 100.25

B. 102.25

C. 104.25

D. 105.25

Problem 26: CE Board May 1995

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side 10 cm long?

A. 104.7

B. 105.7

C. 106.7

D. 107.7

Problem 27: CE Board November 1992

The area of a triangle inscribed in a circle is 39.19 cm² and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

A. 11 cm

B. 12 cm

C. 13 cm

D. 14 cm

Problem 28: CE Board November 1994

The area of a triangle is 8346 sq. m and two of its interior angles are 37°25’ and 56°17’. What is the length of the longest side?

A. 171.5 m

B. 181.5 m

C. 191.5 m

D. 200.5 m

Problem 29: ECE Board April 1998

The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in sq. cm?

A. 59.8

B. 89.5

C. 58.9

D. 85.9

Problem 30: EE Board April 1992

Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part.

A. 30 cm²

B. 31 cm²

C. 32 cm²

D. 33 cm²

Problem 31: ECE Board April 1998

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

A. 72π

B. 23π

C. 64π

D. 16π

Problem 32: ECE Board November 1993

The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units?

A. 12.5

B. 13.5

C. 14.5

D. 15.5

Problem 33: CE Board May 1998

A circle having an area of 452 sq. m is cut into two segments by a chord which is 6 m from the center of the circle. Compute the area of the bigger segment.

A. 354.89 sq. m

B. 363.68 sq. m

C. 378.42 sq. m

D. 383.64 sq. m

Problem 34: ECE Board April 1992

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 9 m and each circle passes through the center of the other. Find the area of the swimming pool.

A. 380 m²

B. 390 m²

C. 400 m²

D. 410 m²

Problem 35: ME Board April 1991

Find the difference of the area of the square inscribed in a semi-circle having a radius of 15 cm. The base of the square lies on the diameter of the semi-circle.

A. 171.5 cm²

B. 172.5 cm²

C. 173.5 cm²

D. 174.5 cm²

Problem 36: ECE Board November 1995

A rectangle ABCD which measures 18 cm. 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. 20.5 cm²

B. 21.5 cm²

C. 22.5 cm²

D. 23.5 cm²

Problem 37: ECE Board April 1998

A trapezoid has an area of 36 m² and an altitude of 2 m. Its two bases have the ration of 4:5. What are the lengths of the bases?

A. 12, 15

B. 7, 11

C. 8, 10

D. 16, 20

Problem 38: EE Board March 1998

A rhombus has diagonals of 32 and 20 inches. Determine its area.

A. 360 in²

B. 280 in²

C. 320 in²

D. 400 in²

Problem 39: ECE Board April 1998

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

A. 10.63

B. 10.37

C. 10.73

D. 10.23

Problem 40: CE Board November 1996

Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225°.

A. 96 sq. m

B. 100 sq. m

C. 94 sq. m

D. 98 sq. m

Problem 41: EE Board October 1992

Determine the area of the quadrilateral shown, OB = 80 cm, AO = 120 cm, OD = 150 cm and Ө = 25°

A. 2721.66 cm²

B. 2271.66 cm²

C. 2172.66 cm²

D. 2217.66 cm²

Problem 42: CE Board October 1997

A quadrilateral has sides 12 m, 20 m, 8 m and 16.97 m. If the sum of the opposite angles is equal to 225°, find the area of the quadrilateral.

A. 100 m²

B. 124 m²

C. 168 m²

D. 158 m²

Problem 43: ME Board October 1996, ME Board April 1997

The area of a regular hexagon inscribed in a circle of radius 1 is?

A. 1.316

B. 2.945

C. 2.598

D. 3.816

Problem 44: EE Board April 1990

Find the area (in cm²) of a regular octagon inscribed in a circle of radius 10 cm?

A. 283

B. 289

C. 298

D. 238

Problem 45: GE Board February 1992

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

A. 36. 45 sq. m

B. 63. 54 sq. m

C. 45. 63 sq. m

D. 54. 36 sq. m

Problem 46: EE Board April 1993

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

A. 1075 m²

B. 1085 m²

C. 1080 m²

D. 1095 m²

Problem 47: ME Board October 1996

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

A. 5.533 in.

B. 5.335 in.

C. 6.335 in.

D. 7.335 in.

Problem 48: EE Board April 1990

In a circle of diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the area of that part not covered by the star?

A. 40.5 sq. m

B. 45.5 sq. m

C. 50.5 sq. m

D. 55.5 sq. m

Problem 49: EE Board March 1998

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

A. 430.70 cm²

B. 573.26 cm²

C. 473.77 cm²

D. 516.14 cm²

Problem 50: EE Board March 1999

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.

A. 441.66 cm²

B. 467.64 cm²

C. 519.60 cm²

D. 493.62 cm²

Online Question and Answer in Plane Geometry Series

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