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:
- A$8\ cm$
- B$36\ cm$
- C$4\ cm$
- ✓$6\ cm$
Answer: D.
View full solution →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
01
M.C.Q
9 Q→02True False[1 Marks ]
9 Q→033 Marks Question
4 Q→045 Marks Questions
3 Q→054 Marks Questions
11 Q→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.
Write the correct answer in the following: The area of an equilateral triangle with side $2\sqrt{3}\text{cm}$ is:
- ✓$5.196 \mathrm{~cm}^2$
- B$0.866 \mathrm{~cm}^2$
- C$3.496 \mathrm{~cm}^2$
- D$1.732 \mathrm{~cm}^2$
Answer: A.
View full solution →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:
- A$48\ cm$
- ✓$24\ cm$
- C$12\ cm$
- D$36\ cm$
Answer: B.
View full solution →Write the correct answer in the following: The perimeter of an equilateral triangle is $60\ m$. The area is:
- A$10\sqrt{3}\text{m}^2$
- B$15\sqrt{3}\text{m}^2$
- C$20\sqrt{3}\text{m}^2$
- ✓$100\sqrt{3}\text{m}^2$
Answer: D.
View full solution →Write the correct answer in the following: The sides of a triangle are $35\ cm, 54\ cm$ and $61\ cm$, respectively. The length of its longest altitude:
- A$16\sqrt{5}\text{cm}$
- B$10\sqrt{5}\text{cm}$
- ✓$24\sqrt{5}\text{cm}$
- D$28\text{cm}$
Answer: C.
View full solution →Write True or False and justify your answer: The area of $\triangle A B C$ is $8 cm^2$ in which $A B=A C=4 cm$ and $\angle A=90^{\circ}$
View full solution →Write True or False and justify your answer: The cost of levelling the ground in the form of a triangle having the sides $51m, 37m$ and $20m$ at the rate of Rs. $3per ~m^2$ is $Rs. 918.$
View full solution →Write True or False and justify your answer: If the side of a rhombus is $10\ cm$ and one diagonal is $16\ cm$, the area of the rhombus is $96\ cm^2.$
View full solution →Write True or False and justify your answer:In a triangle, the sides are given as 1$1\ cm, 12\ cm$ and $13\ cm$. The length of the altitude is $10.25\ cm$ corresponding to the side having length $12\ cm.$
View full solution →Write True or False and justify your answer: The area of the equilateral triangle is $20\sqrt{3}\text{cm}^2$ whose each side is 8cm.
View full solution →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?
View full solution →Find the cost of laying grass in a triangular field of sides $50\ m, 65\ m$ and 65m at the rate of Rs. $7$ per $m^2$.
View full solution →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.
View full solution →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.
View full solution →A design is made on a rectangular tile of dimensions $50cm \times 70cm$ 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.
View full solution →A field is in the shape of a trapezium having parallel sides $90m$ 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 $1m^2 $of the field, find the total cost of ploughing the field.
View full solution →How much paper of each shade is needed to make a kite given in which $ABCD$ is a square with diagonal $44\ cm.$
View full solution →The perimeter of an isosceles triangle is $32\ cm$. The ratio of the equal side to its base is $3 : 2$. Find the area of the triangle.
View full solution →From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14\ cm, 10\ cm$ and $6cm$. Find the area of the triangle.
View full solution →Find the area of the trapezium $PQRS$ with height $PQ$ given in:
View full solution →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.
View full solution →In $\triangle\text{ABC}$ has sides $AB = 7.5\ cm, AC = 6.5\ cm$ and $BC = 7\ cm$. 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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