BERHAN COMPUTER AND TUTORIAL CLASS Chapter Iv 1 . IfABCΞDEF thenCBAΞ_______a.DEFb.EDF c.FDEd.FEDe.none 2.In fig. 1ABC andDBC are two isosceles triangles with the same base BC if AD is extendedto intersect BC at P.Then which of following is not true a.ABDΞACDb.ABPΞACP c. <BADΞ<CADd.AP is a perpendicular bisector of BCe. none 3. In fig. 2it is given that AB=CF,EF=BD and <AFE Ξ <CBD prove thatAFE ΞCB 4. In fig. 4ABC is isosceles triangle withAB =AC and E is the midpoint of BC : prove that AEBC 5. In fig .4line segments AB and CD bisect each other at F show that a. <A Ξ <Bb, AC Ξ DB 6. Prove that the angle bisector of the vertex angle ofAn isosceles triangle is perpendicular at the midpoint of the base. 7.In the fig.5 ABCD is a square. E is the midpoint of CD show that AE ΞBE 8.In fig. 6PQR is an equilateral triangleOR and QL altitudesprove that OR=QL 9. Prove the following theorems: a. A point at equal distance from two points is on the perpendicular bisector of the line segment. b. A point at equal distance from two sides of a triangle is on the angle bisector. C. A line segmentperpendicular to the base of an isosceles triangle passes through the midpoint. d. The pairs of opposite side of a parallelogram are equal. e. The pairs of opposite angles of a parallelogram are equal. f. The diagonals of a rhombus are perpendicular to each other. 9. In fig.3ABC if the height corresponding to base BC =8cm find the length of the height Corresponding to AC: 10. Find the area of the following figures: 11.A plot of land in the shape of an isosceles trapezium (see figure 4) .The areaof the plot is: 12. Two triangles have equal bases. The corresponding height of the one is 5 times that of the the other. Then the ratio of their areas is:a. 5:1b.10:5c.25:1d. 20:5d. none 13.Which of the following is false? a.A rhombus with side 12cm and one angle 1500 has an area of 72sq.cm. b.Two sides of a triangle are 15 and 20 units long. If the altitude to the 15cm side is 8cm Then the altitude to the 20cm side is 6cm. c.The area of a rhombus with diagonals 15 cm and 20 cm is 150sq. cm. d.The two regions into which the medians of a triangle separates the triangular region have Always equal areas.E. none 14.In fig.3 ABCDEF is a regular hexagon of side 8cm then the area of theshaded region is. 15. The area of a regular inscribed hexagon is 27√3cm2then which one is true? a. the length of the side of the polygon is 3cm.b. the radius of the circle is 3 cm c. the perimeter of the polygon is 15 units.d. the circumference of the circle is 8 П e 16 .If r is the radius of a circle inscribed in an equilateral triangle, the area of the triangle is 17.In fig .4 ABCD is a square of side 3cm.If the radius of the circle with center E is 1cm and circle B is 2cm. The perimeter of the shaded part is: 19. The lengths of the sides ofDEF are DE=4cm, EF=6cm and DF= 8cm. The length of the Altitudesto DEDFand EF are? 18.A regular hexagon is inscribed in a circle of radius 6cm .Which of the following is not true? a.The area of the hexagon is 48 √3cm 2 b.The area of the region between the circle and the hexagon is12( 3П- 4√3)cm2
BERHAN COMPUTER AND TUTORIAL CLASS c.The perimeter of the hexagon is36cm d.Area of the triangle formed by joiningany threeconsecutive vertices of the hexagon is 27√3cm2 e.none 20.If the hypotenuse of a 300-600-900triangleis 12cm .which of the following is not true? a.The perimeter of the triangle 18+6√3 cm. b.The length of the altitude to the hypotenuse is 3√3 cm. c.The area of the triangle is 36√3 cm2 . d.The shortest side of the triangle is 6cme. none 21. In the fig. 1 AC=10cm and each shaded triangle is an equilateral triangle, then thetotal area of the shaded region is: 22. The ratio of the areas of inscribed to circumscribed equilateral triangles in a circle is:a.1: 4b.1:3c. √3: 2d . 1: 2e. none 23. In fig. 2the center of the circle is 0 and the radius of the circle is 4cm. The area of the shaded region is: a. 3(П- 2)cm2b. 2(П -3) cm2c. 4(П - 2) cm2d. 2(П - 2) cm2 e. none 24.Two pieces of wire of equal lengths are bent , one in the shape of a square and the other in the shape of an equilateral triangle. What is the ratio of the areas of the regions enclosed by each wires is ; 25.Which of the following is not true? a.An equilateral triangle inscribed in a circle of area4 Пcm2is 4√3cmb. If the length of the hypotenuse of a Right isosceles triangle is x cmthen the length Of its legs is √2x/2cm. c.The area of a square inscribed in acircle of radiusr is 4r2. d. The area of a triangle with sides 25cm, 25cm and 48cm is 168cm2 .e. none 26.The sides of triangle are25cm, 25cm and 48cm a new triangle is formed by joining the mid points of the sidesof the triangle then the area of the new triangle formed 27.In fig 1, what is the area and perimeter of the shaded part? 28. A cylindrical concrete pipe as shown in fig.2of 10m length, inside diameter 60cm and outside diameter 65cm is painted at the costof Nakfa7 per square meter. Find the total cost ofpainting the concrete. a.27,500nkb.2500nkc. 250nkd. 275nke.none 29. In the fig.3 In an equilateralABC of side length 6cm a new triangleDEF is formed by joining the mid points of the sides. Then the ratio of their areas is: a.1:2b. 2:3c. 1:4d.1:3e. none 30.Find the area and perimeter of the shaded regions of each of the following figures AB=4cm 31. A girl wishes to sew a cloth as the pattern in fig. 4 .The tip of each petal is 7cm from the center of the design. Find the area and perimeterof the design? 32. A regular hexagon ABCDEF is inscribed in a circle of radius Xcm. Then the area of the shadedpart in terms of X is: a.[Π- √3] x2cm2b.[ Π- 3√3] x2cm 2 22 c. [Π - 3]x2cm2d.[3- Π] x2cm2e. none 22 33. In fig.4 the center of the semi-circle is O with radius r units If m(arc BP)=2m(arc PA). ThenWhich of the following is true? a. BP= rb. AP= √3/3 rc. the area of the shaded part isr2[Π- 3] c. the area ofABPis 3r2 /2√3e. none2 34. In the fig 5PQ=QR=RS. The diameter of the circle is 12cm .then find the areaand perimeter
BERHAN COMPUTER AND TUTORIAL CLASS of the shaded part 35.Find the area of a sector bounded by an arc of 600in a circle of radius 3√2 cm 36. A swimming pool is 20m in length, 15m in breadth and 4m in depth. Thenthe cost of cementing its floor and walls at a rate of 12Nk per m2. 37. The radius of a cone is 5cm and the height is 13cm. Then the volume of the cone is: a. 65Πcm3b.45Πcm3c. 60Πcm3d. 50Πcm3e. none 38. Find the area and perimeter of the shaded parts below 39.The surface area of a cone ,if its slant height is 25cm and the base diameter is 14cm 40.If the lateral surface area of a cone is 4070cm2and the diameter is 70cm. Then the length of the slant height is; 41. In fig .1 the triangular pyramid AB=14cmAB=11cm and BD=15 cm and h= √6 cm then the volume of the pyramid is: 42. Find the surface area and volume of a square based pyramid with base length 12cm and slant height10cm. 43. Find the volume and surface area of a square based pyramid with base length 10cmand altitude 12cm. **44. How many spherical balls of each 4.2cm in diameter can be obtained from rectangular solid of lead with dimensions66cm, 42cm ,21cm.( use П= 22/7) 44. If a plane intersect a sphere of diameter 26cm at a distance 12cm from the center. Find the radius of the circleformed 45 A metallic spherical balls of radius 3cms is melted and the total substance is utilized to form some equal balls of each with diameter 0.6cm . The number of these smaller balls is: 46.Find the volume and surface area of the following solid figures.