Olympiad – Class IX – Mathematics - Herons Formula

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Question - 1

The perimeter of a triangular field is 144 m and the ratio of its sides is 3: 4: 5. Find the area of the field.

  • A 864 sq.m
  • B 764 sq.m
  • C 854 sq.m
  • D 754 sq.m

Question - 2

One side of an equilateral triangle is 8 cm. What is its area?

  • A \(12\sqrt 3 cm^2\)
  • B \(16\sqrt 3 cm^2\)
  • C \(8\sqrt 3 cm^2\)
  • D \(48\sqrt 3 cm^2\)

Question - 3

The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. What is its area?

  • A 12 sq.cm
  • B 36 sq.cm
  • C 24 sq.cm
  • D 48 sq.cm

Question - 4

The edges of a triangular board are 6 cm, 8 cm and 10 cm. What is the cost of painting it at the rate of 9 paise per cm2?

  • A Rs 2.00
  • B Rs 2.16
  • C Rs 2.48
  • D Rs 3.00

Question - 5

What is the area of a triangle whose sides are 13 cm, 14 cm and 15 cm?

  • A 84 sq.cm
  • B 64 sq.cm
  • C 82 sq.cm
  • D 48 sq.cm

Question - 6

Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 6.5 cm. Find the area of parallelogram.

  • A \(5\sqrt 3\ cm^2\)
  • B \(10\sqrt 3\ cm^2\)
  • C \(15\sqrt 3\ cm^2\)
  • D \(20\sqrt 3\ cm^2\)

Question - 7

The sides of a triangle are in the ratio of 13: 14: 15 and its perimeter is 84 cm. Determine the area of the triangle.

  • A 136 cm2
  • B 236 cm2
  • C 336 cm2
  • D 436 cm2

Question - 8

What is the area of a parallelogram whose diagonal is 6.8 cm and the perpendicular distance of this diagonal from an opposite vertex is 7.5 cm?

  • A 25.5 cm2
  • B 11.9 cm2
  • C 12.5 cm2
  • D 51 cm2

Question - 9

The adjacent sides of a parallelogram are 4 cm and 9 cm. What is the ratio of its altitudes?

  • A 16: 81
  • B 9: 4
  • C 2: 3
  • D 3: 2

Question - 10

The perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm. Determine the length of the other diagonal.

  • A 24 cm
  • B 10 cm
  • C \(2\frac{1}{6} \ cm\)
  • D 12 cm
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