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Area problems


  • 1. If O is the orthocentre of a triangle ABC and ?BOC = 100°, the measure of ?BAC is

  • Options
  • A. 100°
  • B. 180°
  • C. 80°
  • D. 200°
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  • 2. What is the area (in cm2) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

  • Options
  • A. 275/7
  • B. 550/7
  • C. 2200/7
  • D. 1100/7
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  • 3. Triangle PQR is inscribed in the circle whose radius is 14 cm. If PQ is the diameter of the circle and PR = 10 cm, then what is the area of the triangle PQR?

  • Options
  • A. 196
  • B. 30?19
  • C. 40?17
  • D. 35?21
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  • 4. PQR is a right angled triangle in which PQ = QR. If the hypotenuse of the triangle is 20 cm, then what is the area (in cm2) of the triangle PQR?

  • Options
  • A. 100?2
  • B. 100
  • C. 50?2
  • D. 50
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  • 5. PQRS is a square whose side is 20 cm. By joining opposite vertices of PQRS are get four triangles. What is the sum of the perimeters of the four triangles?

  • Options
  • A. 40?2
  • B. 80?2 + 80
  • C. 40?2 + 40
  • D. 40?2 + 80
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  • 6. If ABCDEF is a regular hexagon, then what is the value (in degrees) of ?ADB?

  • Options
  • A. 15
  • B. 30
  • C. 45
  • D. 60
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  • 7. ABCD is square and CDE is an equilateral triangle outside the square. What is the value (in degrees) of ?BEC?

  • Options
  • A. 15
  • B. 30
  • C. 25
  • D. 10
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  • 8. There is a circular garden of radius 21 metres. A path of width 3.5 metres is constructed just outside the garden. What is the area (in metres2) of the path?

  • Options
  • A. 50.05
  • B. 57.56
  • C. 52.12
  • D. none
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  • 9. A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?

  • Options
  • A. 1033
  • B. 1433
  • C. 733
  • D. 2133
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  • 10. In a trapezium, one diagonal divides the other in the ratio 2 : 9. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?

  • Options
  • A. 10
  • B. 5
  • C. 18
  • D. 14
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