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Here we are providing Heron’s Formula Class 9 Extra Questions Maths Chapter 12 with Answers Solutions, Extra Questions for Class 9 Maths was designed by subject expert teachers.

Extra Questions for Class 9 Maths Heron’s Formula with Answers Solutions

Extra Questions for Class 9 Maths Chapter 12 Heron’s Formula with Solutions Answers

Heron’s Formula Class 9 Extra Questions Very Short Answer Type

Question 1.
Find the area of an equilateral triangle having side 6 cm.
Solutioin:
Area of an equilateral triangle = \(\frac{\sqrt{3}}{4}\) × (side)² = \(\frac{\sqrt{3}}{4}\) × 6 × 6 = 9√3 cm²

Question 2.
If the perimeter of an equilateral triangle is 90 m, then find its area.
Solutioin:

Question 3.
If every side of a triangle is doubled, then find the percent increase in area of triangle so formed.
Solutioin:
Let the sides of the given triangle be, a units, b units and c units.

Hence, percent increase = 300%

Question 4.
If the length of a median of an equilateral triangle is x cm, then find its area.
Solutioin:

Let each equal sides of given equilateral triangle be 2y². We know that median is also perpendicular bisector.
∴ y² + x² = 4y²
⇒ x² = 3y²
⇒ x = √3y
or
⇒ y = \(\frac{x}{\sqrt{3}}\)
Now, area of given triangle = \(\frac{1}{2}\)
× 2y × X = y × x = \(\frac{x}{\sqrt{3}}\)× x = \(\frac{x^{2}}{\sqrt{3}}\)

Heron’s Formula Class 9 Extra Questions Short Answer Type 2

Question 1.
Find the area of a triangle whose sides are 11 m, 60 m and 61 m.
Solutioin:
Let a = 11 m, b = 60 m and c = 61 m :

Question 2.
Suman has a piece of land, which is in the shape of a rhombus. She wants her two sons to work on the land and produce different crops. She divides the land in two equal parts by drawing a diagonal. If its perimeter is 400 m and one of the diagonals is of length 120 m, how much area each of them will get for his crops ?
Solutioin:
Here, perimeter of the rhombus is 400 m.
∴ Side of the rhombus = \(\frac{400}{4}\) = 100 m
Let diagonal BD = 120 m and this diagonal divides the rhombus ABCD into two equal parts.

Hence, area of land allotted to two sons for their crops is 4800 m² each.

Question 3.
The perimeter of a triangular field is 144 m and its sides are in the ratio 3:4:5. Find the length of the perpendicular from the opposite vertex to the side whose length is 60 m.
Solutioin:
Let the sides of the triangle be 3x, 4x and 5x
∴ The perimeter of the triangular field = 144 m
⇒ 3x + 4x + 5x = 144
⇒ 12x = 144

Question 4.
Find the area of the triangle whose perimeter is 180 cm and two of its sides are of lengths 80 cm and 18 cm. Also, calculate the altitude of the triangle corresponding to the shortest side.
Solutioin:
Perimeter of given triangle = 180 cm
Two sides are 18 cm and 80 cm
∴ Third side = 180 – 18 – 80 = 82 cm

Hence, area of triangle is 720 cm² and altitude of the triangle corresponding to the shortest side is 80 cm.

Heron’s Formula Class 9 Extra Questions Long Answer Type

Question 1.
Calculate the area of the shaded region.

Solutioin:

= 2 × 2 × 3 × 7 = 84 cm²
Area of shaded region = Area of ∆ABC – Area of ∆AOB
= 84 cm² – 30 cm² = 54 cm²

Question 2.
The sides of a triangular park are 8 m, 10 m and 6 m respectively. A small circular area of diameter 2 m is to be left out and the remaining area is to be used for growing roses. How much area is used for growing roses ? (use n = 3.14)
Solutioin:
The sides of the triangular park are 8 m, 10 m and 6 m.

Radius of the circle = \(\frac{2}{2}\) = 1 m
Area of the circle = πr² = 3.14 × 1 × 1 = 3.14 m²
∴ Area to be used for growing roses = Area of the park – area of the circle
= 24 – 3.14 = 20.86 m²

Heron’s Formula Class 9 Extra Questions HOTS

Question 1.
OPQR is a rhombus, whose three vertices P, Q and R lie on the circle with centre 0. If the radius of the circle is 12 cm, find the area of the rhombus.
Solutioin:
Since diagonals bisect each other at 90°.
∴ In right ∆QLR, (LR)² + (LQ)² = (QR)²

Question 2.
How much paper of each shade is needed to make a kite given in the figure, in which ABCD is a square with diagonal 60 cm?

Solutioin:
Since diagonals of a square are of equal length and bisect each other at right angles, therefore,
Area of ∆AOD = \(\frac{1}{2}\) × 30 × 30 = 450 cm²
Area of ∆AOD = Area of ∆DOC = Area of ∆BOC
= Area of ∆AOB = 450 cm²
[∵ ∆AOD = ∆AOB ≅ ∆BOC ≅ ∆COD, ∵ they² have equal area]
Now, area of ACEF (by Heron’s formula)
Here a = 20 cm, b = 20 cm and c = 30 cm

Now, area of orange shaded paper in kite
= Area of ∆AOD + Area of ∆CEF
= 450 cm² + 198.4 cm²
= 648.4 cm²
Area of blue shaded paper in kite
= Area of ∆AOB + Area of ∆COD
= 450 cm² + 450 cm² = 900 cm²
Area of black shaded paper in kite = Area of ∆BOC = 450 cm².

Heron’s Formula Class 9 Extra Questions Value Based (VBQs)

Question 1.
Sister Nivedita has trapezium shaped plot which she divided into three triangular portion for different purposes. I – for providing free education for orphan children, II – for providing dispensary for the needy villagers and III – for the library for villagers. Find the area of trapezium plot given in the figure. Which qualities of sister Nivedita are being depicted in question ?

Solutioin:
Here, ABCD is the trapezium with AB || DC.
Through C, Draw CF ⊥ AB
For – I: For area of ∆EBC

But, we know, Area of ∆EBC = \(\frac{1}{2}\)(base × height)
⇒ \(\frac{1}{2}\)1 × 30 × CF = 336
15 × CF = 336
⇒ CF = \(\frac{336}{15}\) = 22.4 m
Now, area of trapezium shaped plot = \(\frac{1}{2}\) (20 + 50)(22.4)
= 35 x 22.4 = 784 m²
Caring, kind, social, generous and visionary lady.

Question 2.
In an exhibition, an umbrella is made by stiching 10 triangular pieces of cloth with same message written on two triangular pieces. If each piece of cloth measures 60 cm, 60 cm and 20 cm, find how much cloth is required for each message.
Why we should respect women, educate women, save women and empower women ?

Solutioin:
Here, each triangular piece is an isosceles triangle with sides 60 cm, 60 cm and 20 cm.

Now, there are 2 triangular pieces with same message.
∴ Total area of cloth for each message = 2 × 591.61 = 1183.22 cm²
We should respect women, educate women, save women and empower women to serve humanity and give them equal opportunity so far they deprived.

On this page, you will find NCERT Class 7 Geography Chapter 10 Notes Pdf free download. CBSE Class 7 Social Science Notes Geography Chapter 10 SST Life in the Deserts will seemingly help them to revise the important concepts in less time.

Life in the Deserts Class 7 Notes Social Science Geography Chapter 10

CBSE Class 7 Geography Chapter 10 Notes Understanding The Lesson

1. It is very difficult to live on the places where there is no water.

2. Some places are very hot as fire while some are very cold as ice. These are the desert areas of the world.

3. Depending on the temperatures there can be hot desert or cold deserts.

4. The people inhabit these lands wherever little water is available to practice agriculture.

5. Sahara is the world’s largest desert. Sahara desert covers a large part of North Africa. It has an area of around 8.54 millions km.

6. The Sahara desert touches 11 countries. These are Algeria, Chad, Egypt, Libya, Mali, Mauritania, Morocco, Niger, Sudan, Tunisia and Western Sahara.

7. Besides the vast stretches of sands, there are also gravel plains and elevated plateaus with bare rocky surface. These rocky surfaces may be more than 2500m high at some places.

8. The climate of the Sahara desert is scorching hot and parch dry. It has a short rainy season. Days are unbelievable hot, it may be as high as 50°C while nights may be freezing cold with temperatures nearing 0°C

9. Cactus, date palms and acacia etc., are vegetation found in the Sahara desert. In some places there are oasis-green islands with date palms surrounding them.

10. Camels, hyenas, jackals, foxes, scorpions, many varieties of snakes and lizards are the prominent animal species living there.

11. Despite of harsh climate in the Sahara, it is inhabited by various groups of people who pursue different activities. Some nomadic tribes such as Bedounis and Tuaregs live here and rear goats, sheep, camels and horses.

12. The oasis in the Sahara and the Nile Valley in Egypt suppont the settled population. The people grow date palms, rice, wheat, barley and beans. Egyptian cotton, famous worldwide is grown in Egypt.

13. Besides the oil, other minerals of importance that are found in the area include iron, phosphorus, manganese and uranium.

14. Ladakh is a cold desert lying in the Great Himalayas, on the eastern side of Jammu and Kashmir. The Karakoram Range in the north and the Zanskar mountains in the south enclose it. River Indus and Gangri glacier are found in Ladakh.

15. Ladakh is made up of two words-“La” meaning ‘mountain pass’ and “Dak” meaning ‘country’.

16. The altitude (height) in Ladakh varies from about 3000 m in Kargil to more than 8,000m in the Karakoram. Due to its high altitude, the climate is extremely cold and dry. The day temperatures in summer are just above 0°C and the night temperatures well below-30°C. There is little rainfall, as low as 10 cm every year.

17. Due to high aridity in Ladakh, the vegetation is sparse. There are scanty patches of grasses and shrubs for animals to graze. Groves of Willows and poplars are seen in the valleys. Fruit trees such as apples, apricots and walnuts bloom and are found during the summers.

18. Animals like Robins, redstarts, Tibetan snow-cock, raven and hoopoe are found commonly. The animals of Ladakh are wild goats, wild sheep, yak and special kinds of dogs. Yak’s milk is used to make cheese and butter. The hair of the sheep and goat is used to make wollens.

19. In the summer season the people are busy cultivating barley, potatoes, peas, beans and turnip.

20. Leh, the capital of Ladakh is well-connected both by road and air. The National Highway 1A connects Leh to Kashmir Valley through the Zoji la Pass.

21. Tourism is a major activity with several tourists streaming in from within India and abroad. Visits to the gompas, treks to see the meadows and glaciers, witnessing ceremonies and festivities are important activities.

Notes of Geography Class 7 Chapter 10 Important Terms

Desert: A place of extreme hot or extreme cold.

Glaciers: A glacier is a persistent body of dense ice.

On this page, you will find NCERT Class 7 Geography Chapter 9 Notes Pdf free download. CBSE Class 7 Social Science Notes Geography Chapter 9 SST Life in the Temperate Grasslands will seemingly help them to revise the important concepts in less time.

Life in the Temperate Grasslands Class 7 Notes Social Science Geography Chapter 9

CBSE Class 7 Geography Chapter 9 Notes Understanding The Lesson

1. Forest can be defined as the place where trees are the main type of vegetation. Similarly, grassland can be defined as a region where grasses form the dominant type of plant life.

2. Grasslands make up almost a quarter of the total land surface.

3. The types of plants or grasses are dependent on the climate and soil. ‘

4. The world’s grasslands can be divided into two broad categories-temperate and tropical regions grasslands.

5. The temperate grasslands of North America are known as the Prairies. It is a region of flat, gently sloping or hilly land. Tallgrass, upto two metres high, dominates the landscape. Most part of prairies is treeless.

6. The prairies are bound by the Rocky Mountains in the West and the great lakes in the East. Prairies cover parts of United States of America and parts of Canada. In the USA, the area is drained by the tributaries of Mississippi and the Canadian prairies are drained by the tributaries of Saskatchewan Rivers.

7. The climate is of continental type with extreme temperatures. The summers are warm with temperatures of around 20°C, while in winter -20°C has been recorded in Winnipeg, Canada. In winters a thick blanket of snow covers this region.

8. The annual rainfall is moderate and is ideal for the growth of grass. A local wind “Chinook” blows here.

9. Prairies are practically tree-less. Where water is available, trees such as willows, alders and poplars grow.

10. Places that receive rainfall of over 50 cm, are suitable for farming as the soil is fertile. The major crop of this area is maize, other crops including potatoes, soybean, cotton and alfa-alfa are also grown.

11. Prairies are suitable for cattle rearing. Large cattle farms are called ‘ranches’. Bison or the American buffalo is the most important protected animal of this region. The other animals found in this region are rabbits, coyotes, gophers and prairie dog.

12. The people of the Prairies region are very hard-working. Two of the most developed countries in the world-the USA and Canada are located in this region. Scientific methods of cultivation and use of tractors, harvesters and combines have made North America a surplus food producer.

13. The Prairies are also known as the “Granaries of the world,” due to the huge surplus of wheat production.

14. In the Prairies region dairy farming is another major industry. Dairy farming and extensive agriculture both promote setting up of food processing industries.

15. Large mineral deposits particularly coal and iron are found in this region. A good network of roads, railways and canals in this region has made it the most industrialized region in the world.

16. The temperate grasslands of South Africa are called the velds. Velds are rolling plateaus with varying heights ranging from 600 m to 1100 m. It is bound by the Drakensburg Mountains on the east. To its west lies the Kalahari Desert. On the northeastern part, “height velds’ are located that attain a height of more than 1600m, in some places.

17. The tributaries of rivers Orange and Limpopo drain the region.

18. The velds have a mild climate due to the influence of the Indian Ocean. Winters are cold and dry. Temperatures vary between 5°C and 10°C July is the coldest mouth. Summers are short and warm.

19. The velds receive rainfall mainly in the summer months from November to February.

20. The vegetation cover is sparse. Grasses dominate the landscape. Red grass grows in bush velds. In the high velds acacia and maroola are seen to be growing.

21. The animals of the velds are primarily lions, leopards, cheetah and kudu.

22. In the velds region the main crops are maize, wheat, barley, oats and potato. Cash crops like tobacco, sugar cane and cotton are also grown.

23. In the velds regions, sheep rearing is the most important occupation of the people. Sheep has given rise to the wool industry in the velds. Merino sheep is a popular species and its wool is very warm.

24. Dairy farming is the next important occupation. Cattle are reared in the warmer and wetter regions and the dairy products like butter, cheese are produced for both domestic supply and also for export.

25. The velds have rich reserve of minerals. Iron and steel industry has developed where coal and iron are present. Gold and diamond mining are major occupations of people of this region.

26. Johannesburg is known for being the gold capital of the world. Kimberley is famous for its diamond mines. The mineral rich area has a well-developed network of transport.

Notes of Geography Class 7 Chapter 9 Important Terms

Grasslands: A region where grasses form as a dominant type of plant life.

Veld: The temperate grasslands of South Africa are called the velds.

Prairie: The word originated from Latin word priata which means meadow.

Ranches: Large cattle farms are called ‘ranches’

Cowboys: The men who look the ranches.

Bison: The American buffalo.

Chinook: A type of hot wind that blows in winter.