Math topic中文

Area formula

use of the formula 12absin⁡C\dfrac{1}{2}ab\sin C for the area of a triangle

Practice questions

  1. 1The figure below is made up of 2 squares, ABCD and DEFG. X is a point on GD and Y is a point on DE. BC = 7 cm, FE = 6 cm…
  2. 2In the figure below, ABCD is a trapezium and AD = BC. Each of the statements is either true, false or not possible to te…
  3. 3A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  4. 4The points A, B, C, D and E are shown in the diagram below such that ABC and AED are straight lines and BE = 8\sqrt{8}…
  5. 5在ΔABC\Delta ABC中，∠B=300,AC=25,D\angle B={{30}^{0}},AC=2\sqrt{5},D是ABAB边上的一点，CD=2CD=2，若∠ACD\angle ACD为锐角， ΔACD\Delta ACD的面积为44…
  6. 6已知aa，bb，cc是△ABC\triangle ABC中角AA，BB，CC的对边，SS是△ABC\triangle ABC的面积.若a2+c2=b2+aca^{2}+c^{2}=b^{2}+ac， ((Ⅰ…
  7. 7A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  8. 8With reference to the origin OO, the points AA, PP and QQ have position vectors a\mathbf{a}, p\mathbf{p} and q\mathbf{q}…
  9. 9The figure is made up of a rectangle, a square and a quadrant. Find the area of the shaded part. (Take π=3.14\pi = 3.14) Ans…
  10. 10In triangle ABC, AB = 14.6 cm, BC = 7.6 cm and angle BAC = 31°. Find obtuse angle ACB. Answer ...° area of triangle ABC.…
  11. 11In the rectangle below, find the area of the shaded triangle.
  12. 12Two squares of different sizes are drawn as shown below. An unshaded square is formed where the 2 squares overlap each o…
  13. 13In the figure below, PQRT and PRSU are rectangles. PQ = 8 cm, QR = 6 cm and PR = 10 cm. Find the length of RS. Ans: ___…
  14. 14The figure below is made up of a rectangle and a square. The ratio of the area of the rectangle to the area of the squar…
  15. 15The figure is formed by 3 identical quarter circles and a triangle. The radius of each quarter circle is 8 cm. Find the…
  16. 16一个三角形用斜二测画法画出来的直观图是边长为22的正三角形，则原三角形的面积是()() A. 262 \sqrt {6} B. 464 \sqrt {6} C. 3 \sqrt {3} D. 都不对
  17. 17The area of triangle ABC is 7.5 cm^2. Two of the sides are of length 5 cm and 6 cm respectively. Find the length of the…
  18. 18The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  19. 19The 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…
  20. 20In the figure, ABC and DEF are right-angled triangles. The base of triangle DEF is twice as long as the base of triangle…
  21. 21In the figure, ABCD is a rectangle made up of four triangles. The ratio of the area of triangle ABF to that of the recta…
  22. 22In the figure below, find the area of Triangle XYZ. Ans: ___ cm2^2
  23. 23The 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…
  24. 24Which two figures below have the same area? (Take π=227\pi = \frac{22}{7})
  25. 25The diagram shows a semicircle, centre O, radius 16 cm. Show that angle AOB = 1.287 radians, correct to 3 decimal places…
  26. 26The diagram shows four points P, Q, R and S on level ground. Q is due east of P. Angle SPQ = 40° and angle PSR = 15°. PQ…
  27. 27设△ABC\triangle ABC的内角AA，BB，CC所对边的长分别为aa，bb，c.c.若sin⁡A=2sin⁡B\sin A=2\sin B，c=4,C=π3c=4,C= \dfrac {π}{3}，则△ABC\triangle ABC…
  28. 28The figure below is made up of 2 squares, ABCD and DEFG. XX is a point on GDGD and YY is a point on DEDE. BC=7 cmBC = 7\text{ cm}…
  29. 29In 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…
  30. 30The figure below is made up of two triangles, PRS and PQT. TQ = 4 cm and the length of TQ is half the length of SR. Find…
  31. 31The area of rectangle ABCD is 1728 cm2\text{cm}^2. The length of FE is 56\frac{5}{6} of the length of AD. What is the are…
  32. 32A, B and C are points on the circle centre O and AB = BC. P is the midpoint of chord AB and Q is the midpoint of chord B…
  33. 33Find the area of triangle ABC shown below.
  34. 34In 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…
  35. 35ABL 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…
  36. 36The 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}…
  37. 37The figure below is made up of a circle and a right-angled triangle XYZ. O is the centre of the circle. YOZ is a straigh…
  38. 38The diagram represents a flat plot of land PQRS. Find the area of the land PQRS. Answer ___ m^2 the length of PS. Answer…
  39. 39In the pentagon ABCDE shown, angle BAE = 60° and angle BCD = 45°. AE is parallel to CD, E lies on CB extended and CE = D…
  40. 40A 1 m wide path cuts across a rectangular field along its length and breadth, forming a path as shown. What is the area…
  41. 41The figure below shows an isosceles triangle XYZ, where XY = YZ. WY = 12 cm, YZ = 15 cm and XZ = 18 cm. Find the area of…
  42. 42Leon designed a logo as shown. The logo is made up of two identical small semi-circles, a circle and a big quadrant. YZ…
  43. 43The diagram shows a regular 12-sided polygon inscribed in a circle and a right-angled triangle PQR with length QR=6QR = 6…
  44. 44设复平面上点对应的复数z=x+yi(x∈R,y∈R)(iz=x+yi(x∈R,y∈R)(i为虚数单位))满足∣z+2∣+∣z−2∣=6|z+2|+|z-2|=6，点ZZ的轨迹方程为曲线C1.C_{1}.双曲线C2C_{2}：x2−y2n=1x^{2}- \dfrac {y^{2}}{n}=1…
  45. 45The diagram shows a field ABCD on horizontal ground. Angle ABC = 115°, Angle CAD = 58°, AB = 9 m, BC = 6 m and CD = 11 m…
  46. 46在△ABC\triangle ABC中，角AA，BB，CC的对边分别为aa，bb，cc，asin⁡B−3bcos⁡Bcos⁡C=3ccos⁡2B.(1)a\sin B-\sqrt{3}b\cos B\cos C=\sqrt{3}c{\cos}^{2}B.(1)…
  47. 47在△ABC\triangle ABC中，A=60∘A=60^{\circ}，AB=2AB=2，且△ABC\triangle ABC的面积S△ABC=32S_{\triangle ABC}= \dfrac { \sqrt {3}}{2}，则边BCBC…
  48. 48在ΔABC\Delta ABC中，角AA，BB，CC所对的边分别为aa，bb，cc，若a=7a=7，b=5b=5，c=8c=8，则ΔABC\Delta ABC的面积SS等于 A. 10           10\:\:\:\:\:\:\:\:\:\:\: …
  49. 49The figure below is made up of a square, a quarter circle and a semicircle. The area of the square is 196 cm2^2. Find t…
  50. 50The diagram shows a circle, centre O, radius 10 cm. AB is a chord of length 16 cm. Show that angle AOB = 1.855 radians,…
  51. 51The area of triangle XYZXYZ is 12.6 cm^2. XY=4.5XY = 4.5 cm and YZ=7.1YZ = 7.1 cm. Find two possible values for ∠XYZ\angle XYZ. Giv…
  52. 52A, B, C and D are points on a circle. Line PCQ is a tangent to the circle. Line QE bisects angle AEC and is parallel to…
  53. 53The figures below are drawn on a square grid. Which 2 figures have the same area? Which 2 figures have the same perimete…
  54. 54A strip of paper 60 cm long is folded to form the shape shown below. The difference in area between the strip of paper a…
  55. 55已知椭圆C：x23+y22=1C： \dfrac {x^{2}}{3}+ \dfrac {y^{2}}{2}=1上的动点PP与其顶点A(−3,0)A(- \sqrt {3},0)，B(3,0)B( \sqrt {3},0)不重合． ((Ⅰ))求证…
  56. 56P, Q, R and S are points on a triangular garden. S R Q is a straight line. It is given that PQ=55 mPQ = 55\ \text{m}, RQ=40 mRQ = 40\ \text{m}…
  57. 57In the figure below, EH is a straight line. FH = HG = 12 cm. EF = 20 cm and EH = 16 cm. Find the area of the triangle EF…
  58. 58In Diagram I below, ABCDE is a regular pentagon, centre O. OA=OB=4 cmOA = OB = 4\text{ cm}. (Diagram I and Diagram II are shown…
  59. 59在△ABC\triangle ABC中，已知3sin⁡2B=1−cos⁡2B \sqrt {3}\sin 2B=1-\cos 2B． (1)求角BB的值； (2)若BC=2BC=2，A=π4A= \dfrac {π}{4}，求△ABC\triangle ABC…
  60. 60The figure below is made up of triangle and a rectangle. The area of the rectangle is twice the area of the triangle. 18\frac{1}{8}…