MATHEMATICS PLANE GEOMETRY CE LICENSURE EXAMINATION PROBLEMS PLANE GEOMETRY
TRIANGLES 6.
In trian$le trian$le ABC " A = 45 an1 an$le an$le C = 70 . The si1e opposite an$le C is is 40 m lon$. :hat is the si1e opposite an$le A% &N+3 M ,* (+.4' m 8'.4' m a. c. 8(.() m 84.() m b. d.
7.
The area of a trian$le is 8,346 m2 an1 t#o of its interior an$les are an1 56 17’ . :hat :hat is the len$th len$th of the lon$est lon$est si1e in 37 25’ an1 meters% &N+3 M +* (43.'( ('4.83 a. c. 4,4.)3 4+'.( b. d.
PERIMETER OF PLANE FIGURES 1.
The perimeter of an ellipse is 28.448 units. If the maor a!is is 10 units" #hat is the len$th of the minor a!is% &M'' M ()* + , a. c. b. d.
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AREA OF PLANE FIGURES 2.
The area of a para/ola ha0in$ a /ase #i1th of 10 cm an1 a hei$ht of 27 cm is2 &M+3 M 4)* (4' 5m( (-' 5m( a. c. ( 4)' 5m 4,' 5m( b. d.
3.
A 5ir5le #hose area is 452 cm2 is 5ut into t#o se$ments /6 a 5hor1 #hose 1istan5e from the 5enter of the 5ir5le is 6 cm . 7in1 the area of the lar$er se$ment in cm2. &M+, M 48* 8-(.) 8,.3 a. c. 88. 8--. b. d.
4.
A 5ir5le is 1i0i1e1 into t#o parts /6 a 5hor1" 3 cm a#a6 from the 5enter. 7in1 the area of the smaller part" in cm2" if the 5ir5le has an area of 201 cm2. &N+, M (4* a. c. )4.3 )).( )-., )8.b. d.
5.
A pie5e of #ire ha0in$ a total len$th of 72 cm #as 5ut into t#o une9ual se$ments an1 /ent to form t#o une9ual s9uares. If the total area of the s9uares is 180 cm2" #hat is the 1ifferen5e in the len$ths of the t#o se$ments% &M'( M +* (3 5m 8( 5m a. c. 4 5m (, 5m b. d.
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In trian$le ABC " an$le C = 70 ; an$le A = 45 ; AB = 40 m . :hat is the len$th of the me1ian 1ra#n from 0erte! A to si1e BC % &M+) M (+* 8., m 8.8 m a. c. 8-.4 m 8-.3 m b. d.
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If AB = 15 m" BC = 18 m an1 an1 CA = 24 m " fin1 the point of interse5tion of the an$ular /ise5tor from the 0erte! C . &N+) M 4-* 4(.4 44.) a. c. 43.8 4).+ b. d.
1".
T#o si1es of a trian$le are 50 m an1 60 m lon$. The an$le in5lu1e1 /et#een these si1es is 30 1e$rees. :hat is the interior an$le &in 1e$rees* opposite the lon$est si1e% &M+ M (* +(.-3 +3.-3 a. c. +8.-3 +4.-3 b. d.
11.
In a trian$le BCD" BC = 25 m an1 CD = 10 m. The perimeter perimeter of the trian$le ma6 /e2 &N+ M 48* -( m -' m a. c. + m -4 m b. d.
12.
:hat is the area of a trian$le #hose si1es are 12 cm" 16 cm" an1 21 cm% &N+- M ()* +).) +8.( a. c. +-.8 +4.3 b. d.
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MATHEMATICS PLANE GEOMETRY 13.
In trian$le ABC " AB = 8 m an1 BC = 20 m. One possi/le 1imension of CA is2 &M+, M 4'* 48 + a. c. 44 b. d.
14.
The si1es of a trian$le ABC are AB = 100 cm " BC = 150 cm " an1 CA = 200 cm. =etermine the area of the trian$le. &M++ M 4)* "4-( 5m ( -"(( 5m ( a. c. ( -"(( 5m "-(( 5m ( b. d.
15.
16.
17.
The si1es of a trian$le ABC are AB = 15 cm " BC = 18 cm " an1 CA = 24 cm. =etermine the 1istan5e from the point of interse5tion of the an$ular /ise5tors to line AB. &M++ M (* ).(4 5m 3.-8 5m a. c. 8.-, 5m .() 5m b. d. In a trian$le BCD" BC = 25 m an1 CD = 10 m . The perimeter of the trian$le ma6 /e2 &N++ M 43* -( m + m a. c. -' m -4 m b. d. T#o si1es of a trian$le measure 18 cm an1 6 cm. The thir1 si1e ma6 /e2 &M'' M 4(* 4( 4' a. c. 48 44 b. d.
2".
The three si1es of a trian$le measure 36 cm" 18 cm" an1 24 cm. :hat is the len$th of the me1ian 1ra#n from the lon$est si1e to the opposite 0erte!% &N'4 M (* 4(.8() 5m 4'.4() 5m a. c. 44.(() 5m 48.'3) 5m b. d.
21.
Gi0en a trian$le ABC #ith si1es AB = 30 cm" BC = 36 cm" an1 AC = 4 8 c m. 7in1 the 1istan5e of the point of interse5tion of perpen1i5ular /ise5tors to si1e BC . &M'( M )* 4).+( 5m 4(.8 5m a. c. 4,.(4 5m 4'.3- 5m b. d.
22.
The si1es of a trian$le are 18 cm" 24 cm" an1 34 cm" respe5ti0el6. 7in1 the len$th of the me1ian to the 24-cm si1e" in cm. &M'8 M )* (3.3 (8.3 a. c. (4.+ ('.3 b. d.
23.
Gi0en the si1es of a trian$le ABC 2 a = 36.3 cm " b = 23.9 cm " c = ?. The an$le opposite si1e a is 102.7 . Compute the 0alue of si1e c in 5entimeters. &N'8 M -* 4).() ().-, a. c. ((.)('.3) b. d. °
POLYGONS
1.
T#o si1es of a trian$le measure 14 cm ea5h. :hat is the ma!imum possi/le area of the trian$le% &M'4 M (8* a. c. 4(4 5m( )3 5m( - 5m( +, 5m( b. d.
24.
The sum of the interior an$les of a pol6$on of n si1es is 1080 1e$rees. 7in1 n. &M+- M 48* 4' + a. c. , b. d.
1!.
Trian$le ABC has si1e AB = 160 cm " BC = 190 cm " an1 CA = 190 cm. Point D is alon$ si1e AB an1 AD = 100 cm . Point E is alon$ si1e CA. =etermine the len$th of AE if the area of trian$le ADE is 3 / 5 the area of trian$le ABC . &N'4 M 4'* 4).8 5m 4,(.3 5m a. c. 4)3.( 5m 4-8.+ 5m b. d.
25.
Ho# man6 1ia$onals ha0e an un1e5a$on% &M'( M (-* 33 ) a. c. )3 8) b. d.
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MATHEMATICS PLANE GEOMETRY INSCRIBE# FIGURES
33.
A 5ir5le of ra1ius 8 cm is ins5ri/e1 in a se5tor ha0in$ a 5entral an$le of 80 . :hat is the area of the se5tor% &M'( M 3* 4+).8 5m ( 8(4.3- 5m ( a. c. ( (+4.,3 5m 3-).3( 5m ( b. d. °
26.
27.
:hat is the area in cm2 of the 5ir5le 5ir5ums5ri/e1 a/out an e9uilateral trian$le #ith a si1e of 10 cm lon$% &M+) M 8'* 4'3.4'8.) a. c. 4'4.8 4'(.( b. d. The area of a 5ir5le 5ir5ums5ri/e1 a/out an e9uilateral trian$le is 254.47 m2. :hat is the area of the trian$le in m2% &N+) M * 4').(( ,).38 a. c. ,).+ ,+.8 b. d.
2.
:hat is the ra1ius of the 5ir5le 5ir5ums5ri/in$ an isos5eles ri$ht trian$le ha0in$ an area of 162 cm2% &M+ M 4)* 48.)( 4(.-8 a. c. 43.4, 4).3 b. d.
2!.
A re$ular he!a$on #ith an area of 93.53 cm2 is ins5ri/e1 in a 5ir5le. The area in the 5ir5le not 5o0ere1 /6 the he!a$on is2 &N++ M 4)* 4,.8, 5m ( 4+.)- 5m ( a. c. 4.-( 5m ( 4)., 5m ( b. d.
3".
The perimeter of a trian$le is 58 cm an1 its area is 144 cm2. :hat is the ra1ius of the ins5ri/e1 5ir5le% &N'' M (-* 3.+- 5m ).)( 5m a. c. +.) 5m 8.4( 5m b. d.
31.
32.
34.
A 5ir5le of ra1ius 9 cm is 5ir5ums5ri/e1 a/out a trian$le #hose area is 48.23 cm2. If one si1e of the trian$le measure 18 cm" 1etermine the len$th of the shortest si1e of the trian$le. &M'4 M ('* 3.8- 5m ).3 5m a. c. .3 5m (.83 5m b. d.
A 5ir5le is 5ir5ums5ri/e1 a/out a he!a$on. the he!a$on if the area outsi1e the he!a$on 15 cm2. &N'( M * -8.8 5m( a. c. -(.3 5m( b. d.
=etermine the area of /ut insi1e the 5ir5le is -4.- 5m( -3., 5m(
35.
A 5ir5le ha0in$ an area of 224 m2 is ins5ri/e1 in an o5ta$on. 7in1 the area of the o5ta$on. &M'8 M * (8,. m( (8.8 m( a. c. ( (3).( m (3.- m( b. d.
36.
=etermine the area of a re$ular he!a$on ins5ri/e1 in a 5ir5le ha0in$ an area of 170 cm2. &N'8 M ,* 4+., 5m( 43,.( 5m( a. c. 4(3.4 5m( 43'. 5m( b. d.
$UA#RILATERALS 37.
7in1 the area of a 9ua1rilateral ha0in$ si1es AB = 10 cm " BC = 5 cm" CD = 14.14 cm " an1 DA = 15 cm if the sum of the opposite an$les is e9ual to 225 . &N+ M 4* + 5m( 4'' 5m ( a. c. +3 5m( +, 5m( b. d. °
3.
A 5ir5le of ra1ius 9 cm is 5ir5ums5ri/e1 a/out a trian$le #hose area is 48.23 cm2. If one si1e of the trian$le measure 18 cm" 1etermine the len$th of the other si1e. &N'4 M (-* 3.8- 5m ,.3 5m a. c. 4.3 5m 4-.'+ 5m b. d. <<<<<<< 8 <<<<<<<
The si1es of a 9ua1rilateral are 12 m" 8 m" 16.97 m" an1 20 m" respe5ti0el6. T#o opposite interior an$les ha0e a sum of 225 . 7in1 the area of the 9ua1rilateral in m2. &M+- M 4'* 43 4, a. c. 4 4( b. d. °
MATHEMATICS PLANE GEOMETRY 3!.
T#o si1es of a parallelo$ram measure 68 cm an1 83 cm an1 the shorter 1ia$onal is 42 cm. =etermine the smallest interior an$le of the parallelo$ram. &M'4 M 8* (8.,3+.3) a. c. b. d. 8'.(4(.) °
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