Each equal side of an isosceles triangle is 13cm and its base is 24cm Area of the triangle is:
Question types
Heron’s Formula question types
255 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
255
Questions
7
Question groups
5
Question types
01
M.C.Q
202 Q→02Assertion (A) & Reason (B) MCQ
28 Q→03True False[1 Marks ]
9 Q→042 Marks Questions
1 Q→053 Marks Question
4 Q→065 Marks Questions
7 Q→07Case study (4 Marks)
4 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.
View full solution →
The base and hypotenuse of a right triangle are respectively $5\ cm$ and $13\ cm$ long. It is area is:
View full solution →The area of equilateral triangle of side 'a' is $4\sqrt{3}\text{cm}^2.$ Its height is given by:
View full solution →If the sides of a triangle are doubled, then its area:
The area of a right-angled triangle is $20\ m^2$ and one of the sides containing the right triangle is $4\ cm.$ Then the altitude on the hypotenuse is:
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 $18\ cm$ and its area is $72\ cm^2$ and it’s base is $8\ cm.$
Reason: Area of triangle $=\frac{1}{2} \times$ base $\times$ sheight
Assertion: The height the triangle is $18\ cm$ and its area is $72\ cm^2$ and it’s base is $8\ cm.$
Reason: Area of triangle $=\frac{1}{2} \times$ base $\times$ sheight
- ✓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 area of a triangle 8966.56 whose sides are respectively 150cm, 120cm and 200cm.
Reason: Heron’s formula $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
View full solution →Assertion: The area of a triangle 8966.56 whose sides are respectively 150cm, 120cm and 200cm.
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.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
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 is $6\ cm^2$ whose sides are $3\ cm, 4\ cm$ and $5\ cm$ respectively.
Reason: Area of triangle $= \sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
Assertion: The area of a triangle is $6\ cm^2$ whose sides are $3\ cm, 4\ cm$ and $5\ cm$ respectively.
Reason: Area of triangle $= \sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}.$
- ✓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 →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 6cm then the height of the triangle is 9cm.
Reason: The height of an equilateral triangle is $\frac{\sqrt3}{2}\text{a}.$
View full solution →Assertion: The side of an equilateral triangle is 6cm then the height of the triangle is 9cm.
Reason: The height of an equilateral triangle is $\frac{\sqrt3}{2}\text{a}.$
- Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- Both assertion and reason are true but reason is not the correct explanation of assertion.
- Assertion is true but reason is false.
- Assertion is false but reason is true.
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 sides of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510m. Then the greatest side is 250cm.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
Assertion: The sides of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510m. Then the greatest side is 250cm.
Reason: Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
- Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- Both assertion and reason are true but reason is not the correct explanation of assertion.
- Assertion is true but reason is false.
- Assertion is false but reason is true.
The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a.
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 →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 $\text{ABC}$ 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 3m 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.
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?
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?
View full solution →A zoo is in the shape of an isosceles trapezium.
It is divided into three zones – Zone 1, Zone 2 and Zone 3.
Animals are kept without cages in Zone 1. Zone 2 is for visitors and Zone 3 is reserved for park
authorities.
It is divided into three zones – Zone 1, Zone 2 and Zone 3.
Animals are kept without cages in Zone 1. Zone 2 is for visitors and Zone 3 is reserved for park
authorities.
To avoid the entry of animals in zones 2 and 3, a 1.8 km long wired fencing is installed.
7. Which of the following calculations shows the area for animals?
A. √1.35×0.65×1.15
B. 2.15×0.35×0.65×1.15
C. √3.15×1.35×1.65×1.15
D. √4.30×1.35×0.65×1.15
8. “The area reserved for animals is twice the area reserved for the zoo authorities.” Do you have enough information to support this statement? Explain your answer.
The outer boundary of Zone 1 is made of solid structures in the shape of isosceles triangles of the same size and barbed wires.
The wall consists of 15 such solid structures.
9. Which of the following calculations shows the total area (in square meters) of the solid structures?
A. √50× 50 ×30
B. √130×50×50×30
C. 15√130×50×50×30
D. 15√260×180×180×16
10. What is the area of a triangle with side lengths 20 cm, 20 cm and 8 cm?
Glass buildings can be strengthened using iron frames. A glass structure and its iron frame are
shown below.
shown below.
The frame consists of equal triangles. The dimensions of a triangle are shown below.
1. How much area is enclosed by one triangle?
2. What is the area of part 1 of the frame?
A. 84 m²
B. 1680 m²
C. 3360 m²
D. 3696 m²
3. Is the area of part 1 equal to the area of part 2? Why?
4. Maintenance of the building’s exterior is done by a company. The company charges Rs 750 per square meter per month.
Which of the following calculations represents the monthly maintenance charges?
A. 24 × 12
B. 750 × 24
C. 3024 × 750
D. 6720 × 750
The design on a tile is made of isosceles triangles.
The side lengths of the triangles are 6 cm, 6 cm and 8 cm.
The side lengths of the triangles are 6 cm, 6 cm and 8 cm.
5. How much area of the tile is black?
A. 24 cm²
B. 9√7 cm²
C. 90 cm²
D. 112√5 cm²
6. A tile is made by joining the vertices of four equilateral triangles. The side length of the triangles is 15 cm. What is the area of the tile?
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