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Area problems


  • 1. PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ?ABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm .Then the length of the line joining the mid points of the sides AB and BC is

  • Options
  • A. 4?2 cm
  • B. 5 cm
  • C. 6 cm
  • D. 10 cm
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  • 2. D and E are points on the sides AB and AC respectively of ?ABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ?DEF and ?CBF

  • Options
  • A. 16:25
  • B. 16:81
  • C. 81:16
  • D. 4:9
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  • 3. Diagonals of a Trapezium ABCD with AB || CD intersect each other at the point O. If AB = 2CD, then the ratio of the areas of ?AOB and ?COD is

  • Options
  • A. 4:1
  • B. 1:16
  • C. 1:4
  • D. 16:1
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  • 4. 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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  • 5. 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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  • 6. 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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  • 7. 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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  • 8. 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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  • 9. 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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  • 10. 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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