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Heron’s Formula MATHS - Heron’s Formula

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 36 questions in this chapter.

Question types

Heron’s Formula question types

36 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

36
Questions
5
Question groups
5
Question types
Sample Questions

Heron’s Formula questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
Write the correct answer in the following:
The length of each side of an equilateral triangle having an area of $9\sqrt{3}\text{cm}^2$ is:
  1. 8cm
  2. 36cm
  3. 4cm
  4. 6cm
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Q 2M.C.Q1 Mark
Write the correct answer in the following: The area of an equilateral triangle with side $2\sqrt{3}\text{ cm}$ is:
  • ✓
    $5.196\ cm^2$
  • B
    $0.866\ cm^2$
  • C
    $3.496\ cm^2$
  • D
    $1.732\ cm^2$

Answer: A.

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Q 3M.C.Q1 Mark
Write the correct answer in the following:
If the area of an equilateral triangle is $16\sqrt{3}\text{cm}^2,$ then the perimeter of the triangle is:
  1. 48cm
  2. 24cm
  3. 12cm
  4. 36cm
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Q 4M.C.Q1 Mark
Write the correct answer in the following:
The perimeter of an equilateral triangle is 60m. The area is:
  1. $10\sqrt{3}\text{m}^2$
  2. $15\sqrt{3}\text{m}^2$
  3. $20\sqrt{3}\text{m}^2$
  4. $100\sqrt{3}\text{m}^2$
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Q 5M.C.Q1 Mark
Write the correct answer in the following: The edges of a triangular board are $6\ cm, 8\ cm$ and $10\ cm$. The cost of painting it at the rate of $9$ paise per $\ cm^2$ is:
  • A
    $Rs. 2.00$
  • ✓
    $Rs. 2.16$
  • C
    $Rs. 2.48$
  • D
    $Rs. 3.00$

Answer: B.

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Q 10True False[1 Marks ]1 Mark
Write True or False and justify your answer:
The area of the isosceles triangle is $\frac{5}{4}\sqrt{11}\text{cm}^2,$ if the perimeter is 11cm and the base is 5cm.
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Q 123 Marks Question3 Marks
The area of a trapezium is $475\ cm^2$ and the height is $19\ cm.$ Find the lengths of its two parallel sides if one side is $4\ cm$ greater than the other.
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Q 133 Marks Question3 Marks
A rectangular plot is given for constructing a house, having a measurement of $40\ m$ long and $15\ m$ in the front. According to the laws, a minimum of $3\ m,$ wide space should be left in the front and back each and $2\ m$ wide space on each of other sides. Find the largest area where house can be constructed.
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Q 143 Marks Question3 Marks
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13\ m, 14\ m$ and $15\ m$. The advertisements yield an earning of $Rs. 2000$ per $m^2$ a year. A company hired one of its walls for $6$ months. How much rent did it pay?
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Q 155 Marks Questions5 Marks
A design is made on a rectangular tile of dimensions $50\ cm \times 70\ cm$ as shown in the design shows $8$ triangles, each of sides $26\ cm, 17\ cm$ and $25\ cm$. Find the total area of the design and the remaining area of the tile.
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Q 165 Marks Questions5 Marks
A field is in the shape of a trapezium having parallel sides $90\ m$ and $30\ m$. These sides meet the third side at right angles. The length of the fourth side is $100\ m$. If it costs $Rs. 4$ to plough $1\ m^2$ of the field, find the total cost of ploughing the field.
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Q 184 Marks Questions4 Marks
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14cm, 10cm and 6cm. Find the area of the triangle.
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Q 194 Marks Questions4 Marks
A rhombus shaped sheet with perimeter $40\ cm$ and one diagonal $12\ cm,$ is painted on both sides at the rate of $Rs. 5$ per $m^2.$ Find the cost of painting.
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Q 204 Marks Questions4 Marks
In $\triangle\text{ABC}$ has sides AB = 7.5cm, AC = 6.5cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of $\triangle\text{ABC}$ is constructed. Find the height DF of the parallelogram.
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Q 224 Marks Questions4 Marks
The perimeter of a triangle is 50cm. One side of a triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side. Find the area of the triangle.
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