Olympiad – Class IX – Mathematics - Area of Parallelograms and Triangles

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Question - 1

Two parallelograms are on the same base and between the same parallels. What is the ratio of their areas?

  • A 2:1
  • B 1:2
  • C 1:1
  • D 3:1

Question - 2

ABCD is a parallelogram and 'O' is the point of intersection of its diagonals \(\bar { AC } \) \(\bar { BD} \)  and If the area of ΔAOD = 8 cm2, what is the area of the ΔBOC?

  • A 2 cm2
  • B 4 cm2
  • C 8 cm2
  • D 32 cm2

Question - 3

The area of a trapezium is 24 cm2. The distance between its parallel sides is 4 cm. If one of the parallel sides is 7 cm, what is the measure of the other parallel side?

  • A 5 cm
  • B 8 cm
  • C 12 cm
  • D 7 cm

Question - 4

The area of a square is 36 cm2. If the side of the square is doubled, what is the ratio of area of the original square to that of the new square formed?

  • A 4:1
  • B 4:3
  • C 1:4
  • D 1:2

Question - 5

The area of a rhombus is 60 cm2. lf one of its diagonals is 15 cm, find the other diagonal.

  • A 4 cm
  • B 8 cm
  • C 10 cm
  • D 16 cm

Question - 6

The area of a triangle is 16 cm2. If its base is 8 cm, what is its corresponding altitude?

  • A 4 cm
  • B 8 cm
  • C 18 cm
  • D 12 cm

Question - 7

One of the diagonals of a quadrilateral is 16 cm. The perpendiculars drawn to it from its opposite vertices are 2.6 cm and 1.4 cm. Find its area.

  • A 32 cm2
  • B 40 cm2
  • C 26 cm2
  • D 28 cm2

Question - 8

The ratio of the bases of two triangles is a : b. If the ratio of their corresponding altitudes is c:d, find the ratio of their areas (in the same order).

  • A ac:bd
  • B ad:bc
  • C bd:ac
  • D bc:ad

Question - 9

The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. What is its area?

  • A 36 cm2
  • B 40 cm2
  • C 44 cm2
  • D 108 cm2

Question - 10

In  ΔABC, AB = 8 cm. If the altitudes corresponding to AB and BCare 4 cm and 5 cm respectively, find the measure of BC.

  • A 6.4 cm
  • B 4.6 cm
  • C 5.4 cm
  • D 4.5 cm