Math topic中文

Perimeter area composite

problems involving perimeter and area of composite plane figures

Practice questions

  1. 1A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  2. 2The diagram (not drawn to scale) shows the speed-time graph of a vehicle. The vehicle starts from rest and accelerates u…
  3. 3The diagram below shows the speed-time graph of a bus journey. The bus accelerated from rest at 1.25 m/s^2 to a speed of…
  4. 4In the diagram, POR is a quadrant of a circle with radius 6 cm. OR and PQ are parallel. QR is an arc of a circle with ce…
  5. 5Four squares of side length 44, 77, 99, and 1010 units are arranged in increasing size order so that their left edges…
  6. 6In the diagram, BA and BC are tangents to the circle with centre O. BO meets the circle at D, OA = 10 cm and BC = 28 cm.…
  7. 7一张长方形的纸，它的长是8厘米，宽是6厘米．（1）如果用它剪下一个最大的圆后，剩下的面积是多少平方厘米？（2）如果用它剪下一个最大的半圆，剩下的面积是多少平方厘米？
  8. 8Mr Faizal stays in a terrace house in the east of Singapore. He is considering installing solar panel at his home. He wa…
  9. 9In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  10. 10Find the area of a regular hexagon with each side 7 cm. Answer ... cm^2 Find the interior angle of a regular 15-sided po…
  11. 11The diagram below shows the speed-time graph of a car's journey. For this journey, calculate the acceleration during the…
  12. 12The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  13. 13Triangle PQR is a right-angled triangle with PQ = 10 cm, QR = 6 cm and ∠PRQ = 90°. M is a point on PR such that MR = 5 P…
  14. 14The diagram shows the speed-time graph of two cars, A and B. Car A, starting from rest, accelerates uniformly for 2 seco…
  15. 15一个圆柱形水桶，底面直径3030厘米，高3535米，桶内装有1515厘米高的水。 (1)如果沿着桶口给这个水桶加一道铁箍，需要多长的铁丝？ (2)水与桶接触的面，面积一共是多少平方厘米？ (3)将一个圆锥形的铁块完全浸没水中，水…
  16. 16The diagram shows the speed-time graph of an object over a period of 40 seconds. Calculate the deceleration of the objec…
  17. 17In the non-convex quadrilateral ABCDABCD shown below, ∠BCD\angle BCD is a right angle, AB=12AB = 12 , BC=4BC = 4 , CD=3CD = 3 , and…
  18. 18A factory prints posters for corporate events. The prices of printing posters of different sizes are listed below. The f…
  19. 19The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  20. 20In the diagram, OABC is a parallelogram and D is the midpoint of BC. BE and OC produced intersect at point F. It is give…
  21. 21The diagram shows the positions of 3 points A, B, and C, at sea level. AB = 4.83 km and BC = 7.24 km. The bearing of B f…
  22. 22A, B and C are points (6, 10), (6,6) and (q, 2) respectively. The area of triangle ABC is 16 square units. Show that q =…
  23. 23In the diagram, the points P, Q and R have coordinates (9, -3), (6,1) and (18, -3) respectively. Find the length of PQ.…
  24. 24The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  25. 25ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  26. 26Tyler is tiling the floor of his 12 foot by 16 foot living room. He plans to place one-foot by one-foot square tiles to…
  27. 27The diagram shows a goat tied to a pole at A. The length of the rope attached to the goat is 6 m. A is due west of the c…
  28. 28The diagram below (not drawn to scale) shows the diagram of a medal plaque. The plaque consists of a circle with center…
  29. 29Old MacDonald has a farm with a rock wall around it. The figure shows a portion of his farm where he plans to build two…
  30. 30The diagram shows the speed-time graph of a motorcyclist. The shaded area represents the distance travelled. The distanc…
  31. 31In the diagram, BDCE is a straight line. BD = 4 cm, AC = 10 cm and AB = AD. Given that the area of triangle ABD is 16 cm…
  32. 32In the diagram, OA‾=12 AP‾\overline{OA}=\tfrac{1}{2}\,\overline{AP} and OB‾=14 OQ‾\overline{OB}=\tfrac{1}{4}\,\overline{OQ}. M is the mi…
  33. 33CBEO is a parallelogram. The position vectors of C and E, relative to O, are a\mathbf{a} and b\mathbf{b} respectively.…
  34. 34The diagram shows a semicircle, centre O, radius 16 cm. Show that angle AOB = 1.287 radians, correct to 3 decimal places…
  35. 35The diagram shows the speed-time graph of a cyclist from Town A to Town B. The total distance travelled by the cyclist i…
  36. 36O is the centre of the circle passing through B, E, D and C. Angle DOC=84∘DOC = 84^\circ and angle CBO=54∘CBO = 54^\circ. PQPQ is…
  37. 37An aircraft waiting to land is flying around a triangular circuit ABC. A, B and C are vertically above three beacons, X,…
  38. 38OABC is a trapezium. OA→=a\overrightarrow{OA}=a, OC→=2c\overrightarrow{OC}=2c and CB→=2a\overrightarrow{CB}=2a. OP:PB=1:3OP : PB = 1 : 3.…
  39. 39The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4-by-4 grid…
  40. 40O is the centre of the equilateral triangle. The triangle ABC forms the base of a pyramid. The vertex, X is vertically a…
  41. 41In the diagram, ABCD is a rectangle and E and F are points on AD and BC respectively. The ratio of the area of triangle…
  42. 42OABD is a parallelogram. O is the origin. A is the point (-7, 3) and AB→=(412)\overrightarrow{AB}=\begin{pmatrix}4\\12\end{pmatrix}…
  43. 43The diagram below shows two circles, with the same centre at O. Points A, B and C lie on the bigger circle and point D l…
  44. 44PR is a diameter of the large circle, centre O. QS is a diameter of the small circle, centre O. PQ and RS are tangents t…
  45. 45AC is a diameter of a circle with centre O. AC=2rAC = \sqrt{2}r and AB=BCAB = BC. COB is a semi-circular arc, centre P. What p…
  46. 46A logo, as shown below, has a circle with centre O and radius 2 cm, an equilateral triangle ABC of side 5 cm and an isos…
  47. 47In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, ∠AOB = θ\theta radians, OC = 8 cm and…
  48. 48ABC is a triangle. D is the point on BC such that 3BD = 2DC. Find AD in terms of m and n. Answer ... R is on AD produced…
  49. 49OBC, ADC, AEB and OED are straight lines. OA→=a\overrightarrow{OA}=a and OB→=b\overrightarrow{OB}=b. OB=13OCOB=\dfrac{1}{3}OC, AE:EB=3:2AE:EB=3:2…
  50. 50In the diagram, ACD is a triangle. B is the point on AC such that AB = 10 cm and BC = 4 cm. E is the point on AD where A…
  51. 51The diagram shows four identical blades of a fan, whose centre is O. Arc AB on the fan blade forms an angle of π/6\pi/6 a…
  52. 5222 P, Q and R are three points on level ground such that RPQ forms a right-angled triangle with PQ and RQ measuring 135…
  53. 53The diagram below shows three points, A, B and C on flat ground. AB = 80 m, AC = 100 m and BC = 90 m. C is due east of A…
  54. 54Mr Graham bought a 2-room flat in Sembawang. The floor plan can be modelled as five rectangles as shown below. Calculate…
  55. 55In the diagram, OBC is the sector of a circle, centre O, and angle BOC = 60∘60^\circ. A and D are the midpoints of OB and…
  56. 56The diagram shows the speed-time graph of a particle. Find the speed of the particle when t=12t = 12 s. Answer ...m/s Find…
  57. 57ABL is a park on horizontal ground. A is 1390 m from L on a bearing of 076°. B is 960 m from L on a bearing of 138°. Fin…
  58. 58The diagram shows a triangle ABC with AB produced to D. AB=18 cmAB = 18\,\mathrm{cm}, BC=20 cmBC = 20\,\mathrm{cm}, AC=22 cmAC = 22\,\mathrm{cm}…
  59. 59The diagram represents a flat plot of land PQRS. Find the area of the land PQRS. Answer ___ m^2 the length of PS. Answer…
  60. 60In the pentagon ABCDE shown, angle BAE = 60° and angle BCD = 45°. AE is parallel to CD, E lies on CB extended and CE = D…