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# MCQ in Geometry Part 1 | Mathematics Board Exam

This is the Multiple Choice Questions Part 1 of the Series in 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 Mathematics Board Exam Syllabi

• MCQ in Lines and Planes | MCQ in lane figures | MCQ in Application of Cavalier’s, Pappus and Prismodial Theorems | MCQ in Coordinate in Space | MCQ in Quadratic Surfaces | MCQ in Mensuration | MCQ in Plane Geometry | MCQ in Solid Geometry | MCQ in Spherical Geometry | MCQs in Analytical Geometry

#### Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

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

a. 1

b. 2

c. 2.5

d. 4

Solution:

2. Assuming that the earth is a sphere whose radius is 6400 km. find the distance along a 3 degree arc at the equator of the earthโs surface.

a. 335.10 km

b. 533.10 km

c. 353.10 km

d. 353.01 km

Solution:

3. The angle subtended by an arc is 24ยฐ. 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

Solution:

4. A rat fell on a bucket of water wheel with diameter of 600 cm which traveled an angle of 190ยฐ 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

Solution:

5. 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 18ยฐ and 36ยฐ 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

Solution:

6. A certain angle has a supplement 5 times its compliment. What is the angle?

a. 67.5ยฐ

b. 58.5ยฐ

c. 30ยฐ

d. 27ยฐ

Solution:

7. Each angle of a regular dodecagon is equal to

a. 135ยฐ

b. 150ยฐ

c. 125ยฐ

d. 105ยฐ

Solution:

8. How many sides have a polygon if the sum of the interior angles is 1080ยฐ?

a. 5

b. 6

c. 7

d. 8

Solution:

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

a. 3

b. 4

c. 5

d. 6

Solution:

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

a. 150ยฐ

b. 160ยฐ

c. 170ยฐ

d. 180ยฐ

Solution:

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

a. 12

b. 24

c. 20

d. 48

Solution:

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

a. 200

b. 170

c. 100

d. 158

Solution:

13. Find each interior angle of a hexagon

a. 90ยฐ

b. 120ยฐ

c. 150ยฐ

d. 180ยฐ

Solution:

14. Given a triangle, C = 100ยฐ, a = 15 m, b = 20 m. Find C

a. 26 m

b. 27 m

c. 28 m

d. 29 m

Solution:

15. In triangle ABC, angle A = 45ยฐ and C = 70ยฐ. 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

Solution:

16. In triangle ABC, angle C = 70ยฐ, A = 45ยฐ, 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

Solution:

17. 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

Solution:

18. 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

Solution:

19. 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

Solution:

20. 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

Solution:

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

a. 93.74ยฐ

b. 92.74ยฐ

c. 90.74ยฐ

d. 86.38ยฐ

Solution:

22. 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

Solution:

23. 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.

Solution:

24. 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. 130ยฐ

b. 140ยฐ

c. 150ยฐ

d. 160ยฐ

Solution:

25. 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

Solution:

26. What is the area n 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

Solution:

27. The area of a triangle inscribed in a circle is 39.19 sq. cm 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

Solution:

28. The area of a triangle is 8346 sq. m and two of its interior angles are 37ยฐ25โ and 56ยฐ17โ. What is the length of the longest side?

a. 171.5 m

b. 181.5 m

c. 191.5 m

d. 200.5 m

Solution:

29. The angle of a sector is 30ยฐ 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

Solution:

30. 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 sq. cm

b. 31 sq. cm

c. 32 sq. cm

d. 33 sq. cm

Solution:

31. 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. 72ฯ

b. 23ฯ

c. 64ฯ

d. 16ฯ

Solution:

32. 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

Solution:

33. 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

Solution:

34. 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 sq. m

b. 390 sq. m

c. 400 sq. m

d. 410 sq. m

Solution:

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

a. 171.5 sq. cm

b. 172.5 sq. cm

c. 173.5 sq. cm

d. 174.5 sq. cm

Solution:

36. 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 cm

b. 21.5 cm

c. 22.5 cm

d. 23.5 cm

Solution:

37. A trapezoid has an area of 36 sq. m and an altitude of 2 m. Its two bases have ratio of 4:5. What is the lengths of the bases?

a. 12, 15

b. 7, 11

c. 8, 10

d. 16, 20

Solution:

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

a. 360 sq. in

b. 280 sq. in

c. 320 sq. in

d. 400 sq. in

Solution:

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

a. 10.63

b. 10.37

c. 10.73

d. 10.23

Solution:

40. 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 225ยฐ

a. 96 sq. m

b. 100 sq. m

c. 94 sq. m

d. 98 sq. m

Solution:

41. Determine the area of the quadrilateral shown, OB = 80 cm, AO = 120 cm, OD = 150 cm and ำจ = 25ยฐ

a. 2721.66 sq. cm

b. 2271.66 sq. cm

c. 2172.66 sq. cm

d. 2217.66 sq. cm

Solution:

42. Find the area of a quadrilateral have sides 12 m, 20 m, 8 m, and 16.97 m if the sum of the opposite angles is equal to 225ยฐ, find the area of the quadrilateral

a. 100 sq. m

b. 124 sq. m

c. 168 sq. m

d. 158 sq. m

Solution:

43. 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

Solution:

44. Find the area in sq. cm of a regular octagon inscribed in a circle of radius 10 cm?

a. 283

b. 289

c. 298

d. 238

Solution:

45. 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

Solution:

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

a. 1075 sq. m

b. 1085 sq. m

c. 1080 sq. m

d. 1095 sq. m

Solution:

47. 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.

Solution:

48. In a circle of a 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

Solution:

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

a. 430.70 sq. cm

b. 573.26 sq. cm

c. 473.77 sq. cm

d. 516.14 sq. cm

Solution:

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

a. 441.66 sq. cm

b. 467.64 sq. cm

c. 519.60 sq. cm

d. 493.62 sq. cm

Solution:

### Online Question and Answer in Geometry Series

Following is the list of multiple choice questions in this brand new series:

MCQ in 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
PART 4: MCQ from Number 151 โ 200                                                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                                                         Answer key: PART 5

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