The area of the rhombus is 96 sq m. If one of its diagonals is 16cm, then the length of its another diagonal is:
- A12cm
- B5cm
- C10cm
- D8cm
Question types
Heron’s Formula question types
202 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
202
Questions
8
Question groups
5
Question types
01
M.C.Q
173 Q→02True False[1 Marks ]
9 Q→031 Marks Question
4 Q→04Match the Following.
2 Q→052 Marks Questions
1 Q→063 Marks Question
5 Q→074 Marks Questions
4 Q→08Case 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.
The sides of a triangle are 56cm, 60cm and 52cm long. Then the area of the triangle is:
- A1311cm2
- B1344cm2
- C1322cm2
- D1392cm2
Write the correct answer in the following:
The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is:
The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is:
- A$\sqrt{15}\text{cm}^2$
- B$\sqrt{\frac{15}{2}}\text{cm}^2$
- C$2\sqrt{15}\text{cm}^2$
- D$4\sqrt{15}\text{cm}^2$
Area of the triangle is equal to :
- A$\text{Base}\times \text{Height}$
- B$\text{2(Base}\times \text{Height})$
- C$\frac{1}{2}\text{(Base}\times \text{height})$
- D$\frac{1}{2}\text{(Base}+ \text{Height})$
If the height of a parallelogram having 500cm2 as area is 20cm, then its base is of length.
- A50cm
- B25cm
- C20cm
- D15cm
In a triangle, the sides are given as 11cm, 12cm and 13cm. The length of the altitude is 10.25cm corresponding to the side having length 12cm.
The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a.
The base and the corresponding altitude of a parallelogram are 10cm and 3.5cm, respectively. The area of the parallelogram is 30cm2.
The area of $\triangle\text{ABC}$ is 8cm2 in which AB = AC = 4cm and $\angle\text{A}=90^\circ$
View full solution →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 m2 is Rs. 918.
The base of an isosceles triangle is $x cm$ and its side $y cm$. Find its area.
View full solution →If the sides of an equilateral triangle increase three times then how many percent increases in its area?
The perimeter of a triangular field is 144 m and its sides are in the ratio $3: 4: 5$. Find the area of the field.
View full solution →The length of an altitude in an equilateral triangle is $h cm$, then find its area.
View full solution →| Column 1 | Column 2 | ||
| Q.1. | Area of an equilateral triangle = = __________ | A. | Length × Breadth |
| Q.2. | Area of a rectangle = __________ | B. | Side |
| C. | $\frac{\sqrt{3}}{4}$ (Side) $^2$ |
| Column 1 | Column 2 | ||
| Q.1. | In$\triangle A B C$ , if $\angle B=90^{\circ}$, AB = 5,and BC= 12, then S =__________. | A. | $3 \sqrt{3}$ |
| Q.2. | For an equilateral triangle, if S = 9 cm, then its inradius =__________ | B. | 15 |
| C. | 20 |
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area.
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
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 3m wide for a gate on one side.
Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
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 m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
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?
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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