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Concise Class-9 Area and Perimeter of Plane Figure ICSE Maths Selina Solutions

Concise Class-9 Area and Perimeter of Plane Figure ICSE Mathematics Solutions Chapter-20. We provide step by step Solutions of Exercise / lesson-20 Area and Perimeter of Plane Figure for ICSE Class-9th Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-20 A, Exe-20 B , Exe-20 C and Exe-20 D to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9th Mathematics .

Concise Class-9 Area and Perimeter of Plane Figure ICSE Mathematics Solutions Chapter-20


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Exe-20 A,

Exe-20 B,

 Exe-20 C,

 Exe-20 D,

 


Exe-20 A, Concise Class-9 Area and Perimeter of Plane Figure ICSE Mathematics Solutions

Question 1

Find the area of a triangle whose sides are 18 cm, 24 cm and 30 cm.

Answer 1

Since the sides of the triangle are 18 cm, 24 cm and 30 cm respectively.

s = 18+24+302
= 36

Hence the area of the triangle is

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Concise Class-9 Area and Perimeter of Plane Figure ICSE Maths Selina Solutions Exe-20 A Q-1

= 216 sq cm

again

A =1/2 base x height

hence

216 = 1/2 base x height

216 = 1/2 x 30 x h

h = 14.4 cm

Question 2

The length of the sides of a triangle are in the ratio 3: 4: 5. Find the area of the triangle if its perimeter is 144 cm.

Answer 2

Let the sides of the triangle are

a=3x

b=4x

c=5x

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Given that the perimeter is 144 cm.

hence

⇒ 3x + 4x + 5x =144

⇒ x = 144/ 12

s = (a+b+c )/2

⇒ 12x/2

⇒ 6x =72

⇒ x = 12

The sides are a=36 cm, b=48 cm and c=60 cm

Area of the triangle is

Concise Class-9 Area and Perimeter of Plane Figure ICSE Maths Selina Solutions Exe-20 A Q-2

= 864 sq cm

Question 3

ABC is a triangle in which AB = AC = 4 cm and A = 90o. Calculate:

(i) The area of ABC,

(ii) The length of perpendicular from A to BC.

Answer 3

(i)

Area of the triangle is given by

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

(ii)

Again area of the triangle

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 4

The area of an equilateral triangle is  Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures   sq. cm. Find its perimeter.

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 5

Find the area of an isosceles triangle with perimeter is 36 cm and base is 16 cm.

Solution 5

Since the perimeter of the isosceles triangle is 36cm and base is 16cm. hence the length of each of equal sides are

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Here

It is given that

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Let ‘h’ be the altitude of the isosceles triangle.

Since the altitude from the vertex bisects the base perpendicularly, we can apply Pythagoras Theorem.

Thus we have,

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 6

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

Solution 6

It is given that

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Let ‘a’ be the length of an equal side.

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence perimeter=

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 7

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Solution 7

From ,

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Area ofSelina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Area of Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

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Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Now

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 8

Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and DBC = 90o

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Solution 8

Given , AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and DBC = 90o

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence perimeter=8+10+13+5=36cm

Area of Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Area of  Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Now

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 9

The base of a triangular field is three times its height. If the cost of cultivating the field at 36.72 per 100 m2 is 49,572; find its base and height.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 10

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find:

(i) its area.

(ii) altitude of the triangle corresponding to its largest side.

(iii) the cost of leveling the field at the rate of Rs. 10 per square metre.

Solution 10
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

(ii)

Consider the following figure.

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 11

Each of equal sides of an isosceles triangle is 4 cm greater than its height. IF the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

Solution 11

Let the height of the triangle be x cm.

Equal sides are (x+4) cm.

According to Pythagoras theorem,

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence perimeter=Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Area of the isosceles triangle is given by

Here a=20cm

b=24cm

hence

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 12

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

Solution 12

Each side of the triangle is Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence the area of the equilateral triangle is given by

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

The height h of the triangle is given by
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 13

In triangle ABC; angle A = 90o, side AB = x cm, AC = (x + 5) cm and area = 150 cm2. Find the sides of the triangle.

Solution 13

The area of the triangle is given as 150sq.cm

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence AB=15cm, AC=20cm and

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 14

If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm2; find its perimeter.

Solution 14

Let the two sides be x cm and (x-3) cm.

Now

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence the sides are 12cm, 9cm

and Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

The required perimeter is 12+9+15=36cm.

Question 15

AD is altitude of an isosceles triangle ABC in which AB = AC = 30 cm and BC = 36 cm. A point O is marked on AD in such a way that BOC = 90o. Find the area of quadrilateral ABOC.

Solution 15
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures
Since AB=AC and Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Now

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures


Concise Class-9 Area and Perimeter of Plane Figure ICSE Mathematics Solutions  Ex. 20(B)

Question 1

Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively.

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 2

The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.

Solution 2
Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 3

Calculate the area of quadrilateral ABCD, in which ABD = 90o, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.

Solution 3

Consider the figure:

 

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

From the right triangle ABD we have

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

The area of right triangle ABD will be:

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Again from the equilateral triangle BCD we have Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Therefore the area of the triangle BCD will be:

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Hence the area of the quadrilateral will be:

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Question 4

Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm A = 90o and BC = CD = 52 cm.

Solution 4

The figure can be drawn as follows:

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Here ABD is a right triangle. So the area will be:

Selina Solutions Icse Class 9 Mathematics Chapter - Area And Perimeter Of Plane Figures

Again

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