#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

## Chapter 17: Heron’s Formula

#### Chapter 17: Heron’s Formula Exercise 17.10 solutions [Page 8]

Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm ?

Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm ?

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm ?

In a ΔABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of ΔABC and hence its altitude on AC ?

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle ?

The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?

The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.

A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.

The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Find the area of the shaded region in the given figure.

#### Chapter 17: Heron’s Formula Exercise 17.20, 19.20 solutions [Pages 19 - 20]

Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Area of PQRS = Area of PQR + Area of ΔPQS = (6+9.166)𝑐𝑚2=15.166𝑐𝑚2

The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its are

A park, in the shape of a quadrilateral ABCD, has ∠C = 900, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m How much area does it occupy?

Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.

A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.

Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)

Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Find the area of the blades of thc magnetic compass shown in Fig.. 12.27. (Take √11 = 3.32).

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.

Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD =9 cm, CD = l2cm, ∠ACB = 90° and AC=l5cm.

A hand fan is made by stitching lo equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.

#### Chapter 17: Heron’s Formula solutions [Page 24]

Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.

Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.

Find the area of an isosceles triangle having the base x cm and one side y cm.

Find the area of an equilateral triangle having each side 4 cm.

Find the area of an equilateral triangle having each side* x* cm.

The perimeter of a triangullar field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.

Find the area of an equilateral triangle having altitude *h* cm.

Let Δ be the area of a triangle. Find the area of a triangle whose each side is twice the side of the given triangle.

If each side of a triangle is doubled, the find percentage increase in its area.

If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

#### Chapter 17: Heron’s Formula solutions [Pages 24 - 25]

Mark the correct alternative in each of the following:

The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is

225 cm

^{2}225 \[\sqrt{3}\] cm

^{2}225 \[\sqrt{2}\] cm

^{2}450 cm

^{2 }none above

The base of an isosceles right triangle is 30 cm. Its area is

225 cm

^{2}225 \[\sqrt{3}\] cm

^{2 }225 \[\sqrt{2}\] cm

^{2 }450 cm

^{2}

The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is

- \[12\sqrt{5} c m^2\]
- \[12\sqrt{3} c m^2\]
- \[24\sqrt{5} c m^2\]
- \[63 c m^2\]

The sides of a triangular field are 325 m, 300 m and 125 m. Its area is

18750 m

^{2}37500 m

^{2}97500 m

^{2}48750 m

^{2}

The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is

20 cm

30 cm

40 cm

50 cm

The sides of a triangle are 11 m, 60 m and 61 m. The altitude to the smallest side is

11 m

66 m

50 m

60 m

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is

- \[30\sqrt{7} cm\]
- \[\frac{15\sqrt{7}}{2}cm\]
- \[\frac{15\sqrt{7}}{4}cm\]
30 cm

The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is

25 cm

^{2}28 cm

^{2}30 cm

^{2}40 cm

^{2}

4 cm

- \[\frac{4}{\sqrt{3}} cm\]
- \[\frac{\sqrt{3}}{4} cm\]
3 cm

#### Answer 9:

If the area of an isosceles right triangle is 8 cm^{2}, what is the perimeter of the triangle?

8 + \[\sqrt{2}\] cm

^{2}8 + 4 \[\sqrt{2}\] cm

^{2}4+ 8 \[\sqrt{2}\] cm

^{2}12 \[\sqrt{2}\] cm

^{2}

The lengths of the sides of Δ *ABC* are consecutive integers. It Δ *ABC* has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of Δ*ABC**?*

4

6

8

10

In the given figure, the ratio *AD* to *DC* is 3 to 2. If the area of Δ ABC is 40 cm^{2}, what is the area of Δ* BDC*?

If the length of a median of an equilateral triangle is *x* cm, then its area is

x

^{2}- \[\frac{\sqrt{3}}{2} x^2\]
- \[\frac{x^2}{\sqrt{3}}\]
- \[\frac{x^2}{2}\]

If every side of a triangle is doubled, then increase in the area of the triangle is

- \[100\sqrt{2} \] %
200%

300%

400%

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is \[12\sqrt{2}\] cm, then area of the triangle is

- \[24\sqrt{2} c m^2\]
- \[24\sqrt{3} c m^2\]
- \[48\sqrt{3} c m^2\]
- \[64\sqrt{3} c m^2\]

## Chapter 17: Heron’s Formula

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 17 - Heron’s Formula

RD Sharma solutions for Class 9 Maths chapter 17 (Heron’s Formula) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Mathematics chapter 17 Heron’s Formula are Introduction to Area of a Triangle, Area of a Triangle by Heron’S Formula, Application of Heron’S Formula in Finding Areas of Quadrilaterals.

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