The lengths of three sides of a triangle are $20\ cm, 16\ cm$ and $12\ cm$. The area of the triangle is:
- ✓$96\ cm^2$
- B$120\ cm^2$
- C$144\ cm^2$
- D$160\ cm^2$
Answer: A.
View full solution →Question types
Heron’s Formula question types
252 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
252
Questions
6
Question groups
5
Question types
01
M.C.Q
202 Q→02Assertion (A) & Reason (B) MCQ
29 Q→03True False[1 Marks ]
9 Q→042 Marks Questions
1 Q→053 Marks Question
4 Q→065 Marks Questions
7 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.
The lengths of a triangle are $6\ cm, 8\ cm$ and $10\ cm.$ Then the length of perpendicular from the opposite vertex to the side whose length is $8\ cm$ is:
- A$4\ cm$
- ✓$6\ cm$
- C$5\ cm$
- D$2\ cm$
Answer: B.
View full solution →The sides of a triangle are in the ratio $12 : 17 : 25$ and its perimeter is $540\ cm.$The area is:
- A$1000\ sq.cm$
- B$5000\ sq.cm$
- ✓$9000\ sq.cm$
- D$8000\ sq.cm$
Answer: C.
View full solution →The sides of a triangle are $122m, 22m$ and $120m$ respectively. The area of the triangle is:
- ✓$1320\ sq.m$
- B$1300\ sq.m$
- C$1400\ sq.m$
- D$1420\ sq.m$
Answer: A.
View full solution →If the area of an equilateral triangle is $\sqrt{163}\text{cm}^2$ then the perimeter of the triangle is:
- A$12\ cm$
- ✓$24\ cm$
- C$48\ cm$
- D$306\ cm$
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If $2\text{S}=\frac{(\text{a}+\text{b}+\text{c})}{2}$ where $a,b,c$ are the sides of triangle then area $ =\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
Reason: The sides of triangle are $3\ cm, 4\ cm, 5\ cm$ it’s area is $6cm^2$
Assertion: If $2\text{S}=\frac{(\text{a}+\text{b}+\text{c})}{2}$ where $a,b,c$ are the sides of triangle then area $ =\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
Reason: The sides of triangle are $3\ cm, 4\ cm, 5\ cm$ it’s area is $6cm^2$
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The perimeter of a right angled triangle is $60\ cm$ and its hypotenuse is $26\ cm.$ The other sides of the triangle are $10\ cm$ and $24\ cm.$ Also, area of the triangle is $120 \mathrm{~cm}^2$.
Reason: $(\text { Base })^2+(\text { Perpendicular })^2=(\text { Hypotenuse })^2$.
Assertion: The perimeter of a right angled triangle is $60\ cm$ and its hypotenuse is $26\ cm.$ The other sides of the triangle are $10\ cm$ and $24\ cm.$ Also, area of the triangle is $120 \mathrm{~cm}^2$.
Reason: $(\text { Base })^2+(\text { Perpendicular })^2=(\text { Hypotenuse })^2$.
- ✓Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- BBoth assertion and reason are true but reason is not the correct explanation of assertion.
- CAssertion is true but reason is false.
- DAssertion is false but reason is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The height the triangle is $18cm$ and its area is $72cm^2$ and it’s base is $8cm$.
Reason: $\text{Area of triangle}=\frac{1}{2}\times\text{base}\times\text{height}.$
Assertion: The height the triangle is $18cm$ and its area is $72cm^2$ and it’s base is $8cm$.
Reason: $\text{Area of triangle}=\frac{1}{2}\times\text{base}\times\text{height}.$
- ✓Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The side of an equilateral triangle is $6\ cm$ then the area of the triangle is $9cm^2$.
Reason: All the sides of an equilateral triangle are equal.
Assertion: The side of an equilateral triangle is $6\ cm$ then the area of the triangle is $9cm^2$.
Reason: All the sides of an equilateral triangle are equal.
- A$A$ is true, $R$ is true; $R$ is a correct explanation for $A.$
- B$A$ is true, $R$ is true; $R$ is nol a correct explanation for $A.$
- C$A$ is true; $R$ is false.
- ✓$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The area of a triangle 8966.56 whose sides are respectively $150\ cm, 120\ cm$ and $200\ cm$
Reason: Heron’s formula $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
Assertion: The area of a triangle 8966.56 whose sides are respectively $150\ cm, 120\ cm$ and $200\ cm$
Reason: Heron’s formula $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
- ✓Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →The area of $\triangle\text{ABC}$ is $8\ cm^2$ in which $AB = AC = 4\ cm$ and $\angle\text{A}=90^\circ$
View full solution →The cost of levelling the ground in the form of a triangle having the sides $51 m, 37 m$ and $20 m$ at the rate of $Rs. 3$ per $m ^2$ is $Rs. 918.$
View full solution →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 →In a triangle, the sides are given as $11\ cm, 12\ cm$ and $13\ cm$. The length of the altitude is $10.25\ cm$ corresponding to the side having length $12\ cm.$
View full solution → The area of the equilateral triangle is $20\sqrt{3}\text{cm}^2$ whose each side is 8cm.
View full solution →An isosceles triangle has perimeter $30 \ cm$ and each of the equal sides is $12 \ cm$. Find the area of the triangle.
View full solution →Sides of a triangle are in the ratio of $12: 17: 25$ and its perimeter is $540 \ cm$. Find its area.
View full solution →The sides of a triangular plot are in the ratio of $3 : 5 : 7$ and its perimeter is $300 \ m$. Find its area.
View full solution →A triangular park $ABC$ has sides $120 m, 80 m$ and $50 \ m$ . (in a given figure). A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of ₹ $20$ per metre leaving a space $3$ m wide for a gate on one side.
View full solution →Find the area of a triangle, two sides of which are $8 \ cm$ and $11 \ cm$ and the perimeter is $32 \ cm.$
View full solution →Find the area of a triangle two sides of which are $18 \ cm$ and $10 \ cm$ and the perimeter is $42 \ cm.$
View full solution →There is slide in a park. One of its side walls has been painted in some colour with a message $KEEP \ THE \ PARK \ GREEN \ AND \ CLEAN$, (see figure). If the sides of the wall are $15 \ m, 11 \ m$ and $6 \ m$, find the area painted in colour.
View full solution →The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122 m, 22 m$ and $120 m$ (see Fig.). The advertisements yield an earning of ₹ $5000$ per $m^2$ per year. A company hired one of its walls for $3$ months. How much rent did it pay?
View full solution →A traffic signal board, indicating $SCHOOL AHEAD$, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula. If its perimeter is $180 \ cm$, what will be the area of the signal board?
View full solution → Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is $400 \ m$ and one of the diagonals is $160 \ m$, how much area each of them will get for their crops?
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