# RD SHARMA Solutions for Class 9 Maths Chapter 17 - Heron's Formula

## Chapter 17 - Heron's Formula Exercise Ex. 17.1

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

Let the sides of triangle be 25x, 17x, and 12x.

Perimeter of this triangle = 540 m

25x + 17x + 12x = 540 m

54x = 540 m

x = 10 m

Sides of triangle will be 250 m, 170 m, and 120 m.

^{2}.

The perimeter of right triangle is 300m. 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 base is (3/2) 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 fig.12.12

## Chapter 17 - Heron's Formula Exercise Ex. 17.2

AC

^{2}= AB

^{2}+ BC

^{2}

(5)

^{2}= (3)

^{2}+ (4)

^{2}

So, ABC is a right angle triangle, right angled at point B.

Area of ABC

Perimeter = 2s = AC + CD + DA = (5 + 4 + 5) cm = 14 cm

s = 7 cm

By Heron's formula

Area of triangle

= (6 + 9.166) cm

^{2}= 15.166 cm

^{2}= 15.2 cm

^{2}(approximately)

^{o}, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

In BCD applying Pythagoras theorem

BD

^{2}= BC

^{2}+ CD

^{2}

= (12)

^{2}+ (5)

^{2}

= 144 + 25

BD

^{2}= 169

BD = 13 m

= 35.496 + 30 m

^{2}

^{2}

^{2}(approximately)

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

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 m^{2}. Find the cost of painting.

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 the magnetic compass shown in fig.

(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.

A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in fig., 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 Exercise 17.24

The side of triangle are 16 cm, 30 cm, 34 cm, its area is

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

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

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

(a) 18750 m^{2}

(b) 37500 m^{2}

(c) 97500 m^{2}

(d) 48750 m^{2}

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

(a) 20 cm

(b) 30 cm

(c) 40 cm

(d) 50 cm

## Chapter 17 - Heron's Formula Exercise 17.25

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

(a) 11 m

(b) 66 m

(c) 50 m

(d) 60 m

(a) 4

(b) 6

(c) 8

(d) 10

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

(a) 25 cm^{2}

(b) 28 cm^{2}

(c) 30 cm^{2}

(d) 40 cm^{2}

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