Page 64 - WCS - Electrical

20
130
50 +
=

2 20
130
50 +
50 +
60 + = 60
20 50+
130 = 13020+
=
2
=
=
= 65 cm
2
2
2
= 65 cm
b)
= 65 cm a)(s sx
(s −

−
(s −
c) unit
=
= 65 cm
2
(s −
(s −

a)
= sx
(s −

b)
c) unit

a)

b)
= sx
(s − (s s
−
c) unit c)(s b)
−
a)
(s −x
2
Area A Area A
=

60)(65
-
-
50)(65
65(65
20)
-
=

50)(65
-
65(65
60)(65
-
=

65(65
20)
-50)(65
20)
-
50)(65-(65
60)(65-65(65
-60)
=
=
x
= 65
5
15
6 Find the area of an equilateral triangle whose side is

=
15
x
x
5
265
x
= 468.4 cm

5
5 cm. 6 Find the area of an equilateral triangle whose side is Area A Area A = 60 + x 2 60 + x = 2 45 (s − (s − x 45 - - 2 20) unit 2 2
x
x
15
x 5x
45 15 x
45
= 65 = 65
= 468.4 cm
6 Find the area of an equilateral triangle whose side is Area of polish on both sides = 2 x 468.4 2 2
6 Find the area of an equilateral triangle whose side is
5 cm.

= 468.4 cm
2
5 cm. 5 cm. 3 = 468.4 cm
Area of polish on both sides = 2 x 468.4
= 936.8 cm
Area = a unit 3 Area of polish on both sides = 2 x 468.4 2
2
2

Area of polish on both sides = 2 x 468.4
WORKSHOP CALCULATION & SCIENCE - CITS
4

= 936.8 cm
Area 3 = 3 a unit 2 Cost of polish per 100 cm 2 = Rs. 1.35 2
2
= 936.8 cm
=
Area Area 4 a unit 4 a unit 2 Cost of polish per 100 cm 2 = 936.8 cm 2
2
2
2
=
2
1.732
= Rs. 1.35
4
936.8
= x 5 x 5 ∴ Cost of polish is 936.8 cm 2 2 = = Rs. 1.35
Cost of polish per 100 cm
= Rs. 1.35
Cost of polish per 100 cm
2
1.732
4
x 1.35
1.732 = 1.732 x 5 x 5 100 936.8
= 10.825 cm 4 ∴ Cost of polish is 936.8 cm 2 x 1.35
=
936.8= 936.8
x 5 x 5 x 5 x 5
=
2
x 1.35
4 4 2 ∴ Cost of polish is 936.8 cm 2 = = Rs. 12.65 100 x 1.35
=
∴ Cost of polish is 936.8 cm
2
= 10.825 cm
100
100
7 Calculate its perimeter if one side of an equilateral 10 Find the area of the right angled triangle with base 20
= 10.825 cm
= Rs. 12.65
2
= 10.825 cm
2
= Rs. 12.65
triangle is 55 mm long. cm and height 8 cm. = Rs. 12.65
7 Calculate its perimeter if one side of an equilateral
10 Find the area of the right angled triangle with base 20
7 Calculate its perimeter if one side of an equilateral 10 Find the area of the right angled triangle with base 20
7 Calculate its perimeter if one side of an equilateral
10 Find the area of the right angled triangle with base 20
triangle is 55 mm long.
cm and height 8 cm.
Side
= 55 mm
= 20 cm
Base b
triangle is 55 mm long. 10 Find the area of the right angled triangle with base 20 cm and height 8 cm.
triangle is 55 mm long.
cm and height 8 cm.
cm and height 8 cm.
Perimeter (P) Side = 55 mm Equal sides or = 20 cm
= ?
Base b
Side
= 55 mm = 55 mm
Side
Base b Base b
= 20 cm = 20 cm
Perimeter (P) = ? slant height = 8 cm
= 3a unit
Equal sides or
P
= ?
Perimeter (P) P = ? Area (A) = ? = 8 cm
Perimeter (P)
Equal sides or
Equal sides or
slant height
= 3a unit
slant height
P = 3 x 55 slant height = 8 cm = 8 cm
= 3a unit = 3a unit
P
Area (A)
= 3 x 55
= 165 mm Area (A) Area (A) = ? = ?
1
= ?
= 3 x 55 = 3 x 55 Area (A) = x base x height unit 2
= 165 mm 2 1
= 165 mm
8 Find the area of the triangle having its sides are 9cm, Area (A) 1 = x base x height unit 2
= 165 mm
1
=
2 x base x height unit
10cm and 12 cm. Area (A) Area (A) = x base x height unit 2 2
1
8 Find the area of the triangle having its sides are 9cm,
2
2
8 Find the area of the triangle having its sides are 9cm, = x 20 x 8
8 Find the area of the triangle having its sides are 9cm,
10cm and 12 cm.
1
2
10cm and 12 cm. a + b + c 1 = x 20 x 8
10cm and 12 cm.
1
Semi Perimeter = a + b + c = 80 cm 2 x 20 x 8
unit
= x 20 x 8
=
2
2
b + =
Semi Perimeter c a + b + c unit 2 2 2
a +
= 80 cm
unit 2
Semi Perimeter = 9 + 10 + 12 31 unit 11 Find the area of the right angled triangle if the sides
Semi Perimeter =
2
= 80 cm = 80 cm
2
=
= 2 9 + 2 10 31 containing the right angle being 10.5 cm and 8.2 cm.
11 Find the area of the right angled triangle if the sides
2 12+
2
11 Find the area of the right angled triangle if the sides containing the right angle being 10.5 cm and 8.2 cm.
11 Find the area of the right angled triangle if the sides
10 +
9 + = 9 3112+ = 31 11 Find the area of the right angled triangle if the sides
containing the right angle being 10.5 cm and 8.2 cm.
12 10+
=
1
= 15.5 cm = =2 = 2 containing the right angle being 10.5 cm and 8.2 cm.
containing the right angle being 10.5 cm and 8.2 cm.
2
2 = 15.5 cm 2 Area (A) = x base x height unit 2
2
1
2
= 15.5 cm (s a)(s sx
−
b)
Area (A)
Area A = − = 15.5 cm (s − c) unit 2 Area (A) Area (A) = x base x height unit 2 2 2
= x base x height unit
1
1
Area A = sx (s − a) (s − b) (s − c) unit 2 1 = 2 x base x height unit
2
2

= sx
(s − (s −
=
Area A = 15.5(15.5 - (s −x a) (s − (s s - − b) a) c) unit c)(s b) 12) − 2 unit 2 = x 10.5 x 8.2
Area A
10)(15.5
9)(15.5
-
1
2
1
= x 10.5 x 8.2
1

= x 10.5 x 8.2
=
= 15.5(15.5 - 9)(15.5 - 10)(15.5 - 12) = 43.05 cm 2 x 10.5 x 8.2
2

=
12)
-
=
9)(15.5 -
- 9)(
= 15.5(15.5 15.5(15.5 x 10)(15.5 -15.5 3.5 - 10)(15.5 - 12) 2 2
x
5.5
6.5
15.5x
= 43.05 cm
2
= 15.5x 6.5 x 5.5 x 3.5 12 Calculate the perpendicular height of the triangle if the
= 43.05 cm
= 43.05 cm
2
2
=
15.5x =
= 1939.4375 5.5 6.5 3.5 5.5 x x 3.5 area of the right angled triangle is 19.44 m and its one
x
x
6.5 15.5x
2
12 Calculate the perpendicular height of the triangle if the
12 Calculate the perpendicular height of the triangle if the
of the adjacent side containing the right angle being
= 12 Calculate the perpendicular height of the triangle if the area of the right angled triangle is 19.44 m² and its one
12 Calculate the perpendicular height of the triangle if the
area of the right angled triangle is 19.44 m and its one
2
of the adjacent side containing the right angle being 5.4 m.
= 44.03 cm 21939.4375 5.4 m. area of the right angled triangle is 19.44 m and its one
=
=
area of the right angled triangle is 19.44 m and its one
2
2
1939.4375
1939.4375
of the adjacent side containing the right angle being
= 44.03 cm 2 of the adjacent side containing the right angle being
of the adjacent side containing the right angle being
5.4 m.
9 Find the cost of polishing on both sides of a triangular 5.4 m. 5.4 m.
= 44.03 cm
= 44.03 cm
2
1
2
metal plate has sides 60 cm, 50 cm and 20 cm at the x base x height unit 2 = Area
9 Find the cost of polishing on both sides of a triangular
rate of Rs.1.35 per 100 cm
9 Find the cost of polishing on both sides of a triangular 2 1 1 x base x height unit 2 = Area
2
9 Find the cost of polishing on both sides of a triangular
1
metal plate has sides 60 cm, 50 cm and 20 cm at the
2 x base x height unit
1
2
metal plate has sides 60 cm, 50 cm and 20 cm at the x base x height unit 2 = Area = Area
metal plate has sides 60 cm, 50 cm and 20 cm at the
rate of Rs.1.35 per 100 cm
2
a +
rate of Rs.1.35 per 100 cm 2 b + c 2 2 2 x 5.4 x h = 19.44
rate of Rs.1.35 per 100 cm
1
Semi Perimeter = a + b + c 2 1 1 x 5.4 x h 19.44 = 19.44
unit
x
2
2
2 x 5.4 x h
= 19.44= 19.44
Semi Perimeter c a + b + c unit x 5.4 x h = 19.44 x 2
b + =
a +
h
2
Semi Perimeter = unit 2 unit 2 h = 5.4
Semi Perimeter =
st
2
62 WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25
2
5.4
= 7.2 m
st
62 WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25
st
st
62 62 WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25
= 7.2 m
13 Calculate the base of a right angled triangle having an
area of 15 cm . If its height is 3.5 cm.
13 Calculate the base of a right angled triangle having an
13 Calculate the base of a right angled triangle having an area of 15 cm². If its height is 3.5 cm.
2
area of 15 cm . If its height is 3.5 cm.
2
1
x base x height unit
= Area
1 x base x height unit 2 2 = Area
2
2 What is the length of the hypotenuse of a right angled
2 1 2 What is the length of the hypotenuse of a right angled
triangle, when the sides containing the right angles
= 15
x b x 3.5
1 x b x 3.5 = 15 triangle, when the sid
are 10 cm and 12 cm.es containing the right angles
2
2 are 10 cm and 12 cm.
x 15 2
b = x 15 2
3.5
b = 3.5
= 8.57 cm
= 8.57 cm
Pythagoras theorem
Pythagoras theorem 51
In a right angled triangle the area of the square drawn with
In a right angled triangle the area of the square drawn with
the hypotenuse as the side is equal to the sum of the
CITS : WCS - Electrical - Exercise 5
the hypotenuse as the side is equal to the sum of the
areas of the squares drawn with the other two sides.
areas of the squares drawn with the other two sides.
As per pythagoras theorem,
As per pythagoras theorem, 2
AC
= AB + BC
2
2
AC 2 = AB + BC 2
2
= 10 + 12
2
2
= 10 + 12 2
2
= 100 + 144
= 100 + 144
= 244
= 244
AC = 244
AC = 244
= 15.62 cm
= 15.62 cm
B∠ = 90º 3 Find the height of a right angled triangle whose base is
15 cm and hypotenuse is 21 cm.
B∠ = 90º 3 Find the height of a right angled triangle whose base is
AC = Hypotenuse 15 cm and hypotenuse is 21 cm.
AC = Hypotenuse
AB & BC = Adjacent sides
AB & BC = Adjacent sides
As per pythagoras theorem,
As per pythagoras theorem, 2
= AB + BC
AC
2
2
AC 2 = AB + BC 2
2

2
∴ AC = AB + BC 2

2
∴ AC = AB + BC 2
1 Calculate the hypotenuse of a right angled triangle
1 Calculate the hypotenuse of a right angled triangle
whose base is 5 cm and height is 12 cm.
whose base is 5 cm and height is 12 cm.
As per pythagoras theorem, As per pythagoras theorem,
As per pythagoras theorem,
AC 2 = AB + BC 2 As per pythagoras theorem,
2
AB + BC = AC
2
2
2
AC 2 = AB + BC 2 2 2 2
2
= 12 + 5 2 AB + BC = AC 2
2
AB + 15
= 21
2
2
= 12 + 5 2 AB + 15 2 2 = 21 2
2
2
= 144 + 25
= 144 + 25 AB 2 = 441 - 225
= 169 AB = 441 - 225
= 216
= 169 = 216
AC = 169 AB =
AC = 169 AB = 216
216
= 13 cm = 14.7 cm
= 13 cm = 14.7 cm
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25 63
st
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.25 63
st