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(0975-2087226/092¢ EDGE CE REVIEW SPECIALIST ard Floor, JPD Building, +955 ©. M, Recto Ave,, Samaatee, Manila 19980 |smsrledyeucereviewspecia st@y ral. com MASTERY GUIDES IN PLANE & SOLID GEOMETRY (6 >) Polygons As lhe number of sides of a polygon increases frem 2 lon, (he surn of Lhe exlerior angles lermed by exlending eaeh side in succession: A. increases B. decreases. ©. remains constant D. becomes in-! straight angles How many sides has a polygon il Lwice the sum of ils interior angles equals Ihrice the sum cf ils exterior angles? Ag B.5 C4 c.6 ILis said lnal a polygon has 209 diagonals. Determine the perimeler of this polygen il each side has a length of 8 unils, A176 B716 C167 D871 The apothem of a regular undecagen is @. Determine ils area A. 206.71 sq. unils B. 261.07 sq. unils ©. 170.62 sq. unils D. 127.80 sq. units A regular hexagon ig inscribed in a circle whose radius ig 10. Find Une area of the hexagon. A. 307.12 sq. unils ©. 108.18 sq. units B. 259.81 sq. unils 0. $18.72 sq. unils Find the area of a regular oclagon whose sides measure 8 om, A. 108.81 om? B. 138.67 om? ©. 148.85 om? DB. 120.71 om? Acirsle wilh radius ris inscribed in a hexagon. ig inscribed Lo a larger cirele of radius R. Determine the exacl valug of Ry Ava/3 B which Quadrilaterals Thig refers lc a quadrilaleral wilh oppesile equal acule angles, oppesile equal obluse angles, and four equal sides A. square ©. rhombus B. parallelogram D. lrapezcid The length of the side of a rhombus is 10 cm. If ils sherler diagonal is of langth 12 cm. hal is lhe area of the rhombus? A.S4om? B. 27m? C.48 cm? DC. 96 om? Find lhe area of a rhombus having an angle of 6° i the longer diagonal has length 12 a1 B.12v3 C24 BD. 2av3 The diagonals of a parallelogram are 18 cr and 30 cm respectively. One side of a parallelogram is 12 cm. Find the area of the parallelogram A. 214cm’ B.361.¢m? ©. 216 cm’ B. 108 cm? This refers lo @ quadrilaleral wilh only bo parallel sides. Find (he area cf an iscsceles lrapezoid if the bases have lenglhs 22 and 10, and (he legs have length 10. A128 8.182 C812. 821 In (riangl ABC we have AB = 7, AC = 8, BC =9. Paint Dis on the circumscribed circle of the Iriangle so Uval AD bisecls angle A. Whal ig the value of ADYCD? A98 B.5/9 C.1/7 B52 cles This refers lo a parl al circle or a curve belween bwo points A. sector Care B. segment, C. The central angle of an arc describing a secloris 1/6 radians. If ils radius ig 18 cm, determing (he area of (he seclor A598 8.89.5 ©.58.9 0.85.9 A circle having an area of 452 m’ is cul into two segmenls by a chard which is 6 m [rem the center of Une circle, Compule for the area of the larger segment. A. 354.8 mm? ©. 365.6 m? B. 378.4 m? D. $83.6 m? Chords 4B and CD of a given circle are perpendicular lo each olher and inlersecl al a righl angle al point E Given [hal BE=16, DE=4, and AD=6, find CE. A10 B12 C14 2.16 The radii of be circles thal are langenl externally are @ inches and 8 inches raspestively. Whal ig Une dislance between (he poinls of langency af one of Uneir common external langents? A.G8in B.108in C.11.2in B.12.8in Two circles have radius of 4 cm and 12 em, respeclively. Il \he dislance belween their centers is 20 mm, compule the lengih of the common internal langent le Une Wwe circles. A.27.32 8.28.57 C877 0D. 24.06 The perimeler of a square inscribed in a circle is p. ‘Whal is Une arza ef the square Unal cireurnscribes the circle? Api B. py C. psa An enginger places his (ransil along Lhe ling langent lo the cirgle al pink A such thal PA = 200 m. He locales anolher point B on the sircle and finds PB 0 m. If'a third porlign ©, on the circle lies alang PB, how far from point B will il be? \A. 500m B.480.m C.450m DB. 420 m ) Ga Prisms and inders This refers le @ polyhedron comprising an n-sided polygonal base, a second base which is a lranslaled Copy ‘rigidly moved wilhoul rotation? of the firsl, and n other faces inecessarily all parallelograms) joining corresponding sides of the lwo bases A. prismeid ©. prism, B. pyramid C. cylinder D. p16 Whal is Une volume of a hexagonal prism 18 om high and wilh one of ils sides equal lo & cm? A. square ©. rhombus Ao CESCiP © 810 on B. parallelogram ——_D. trapezoid ) e 1405 cm 0.1205 em S A cylindrical glass wilh base diameler of 6 cm contains waler. A slong was dropped inside the glass and the waler level rises by 2 om. Determine Ihe volume of the slong in cubic centimeter, Ate B91 Cm Bb. 100 ramids, Cones and Frustums In a Lriangular pyramid ABCD, edge AB has length 3 om. The area of lace ABC is 15 cin and the area of face ABD is 12 cnn’. These bwo faces meel gach alher ala20° angle. Find the volume of the pyramid in cnt A.15 em B. 35 em ©. 20 em DB. 60 em The inside diameters af the base of a pol are 10 and 7 inches respeclively, wilh a slant heigh| of 9 inches How many cubic inches of earth does il contain when il is completely lille? A495.6 8.5088 C4827 D.637.5 en , (Spheres \ A sphere of radius $ cm and a righl circular cone of base radius 5 cm and height of 10 om sland on a plane. Find the posilicn on Une plane thal culs the bo solids in equal circular sections. A.1.5om B.25om C.2.0cm B.3.0om A spherical segmenl ig the solid defined by culling a sphere wilh a pair of parallel planes. The surface of (he spherical segment fexcluding (he bases! is called B. wedge Clune D. cone A spherical wooden ball 15 om. in diameler sinks le a depth of 12 om. in @ carlain liquid. Find Une area exposed above Une liquid AsOu 8.25. C48 DL 1S, A spherical wooden ball 15 om. in diameler sinks le a depth of 12 cm. in a certain liquid. Find the volume of the submerged portion in Une liquid AS04n B. 245 C145 B. 12511 The central angle of @ spherical wedge is 1 radian Find its volume ifils radius ig 1 unil. AS B12 0.8/4 D.2 Similarity and Polyhedrons A wooden cone of allilude 10 emis lo be sewed inlo two parls of equal weighl. How many cm fram the verlex should Une cul be parallel le base be made? AL 6.44 B. 7.44 C.6.94 0.7.94 One of the faces of an oclahedron is an equilateral lriangle whese side is 10 m. compule Ihe volume in cubic metge cl the given oclahedran. A495.5 8.4605 C4444 0.4714 eS eg ee s* 5 AD ASTRA PER ASPERA 
