H M. Most of sailboats have two sails, a jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sail boats to the nearest tenth. 8.9 m 22 m 16.8 m 23.9 m 25 m 16,8 m 19.5 m 8.6 m 9.6 m 22.3 m 12.4 m 20 m 10.9 m 3 m C. b. a.
Answers
Step-by-step explanation:
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Question 66
Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.
Solution
In the sailboat (i),
Area of triangle
=
1
2
×
B
a
s
e
×
H
e
i
g
h
t
In
Δ
A
B
C
, AC = Base = 22 + 20 = 42 m
BD = Height = 22.3 m
∴
Area of
Δ
A
B
C
=
1
2
×
42
×
22.3
=
936.6
2
=
468.3
m
2
In another triangular part,
In
Δ
A
C
E
,
E
F
=
H
e
i
g
h
t
=
16.8
m
AC = Base = 22 + 20 = 42 m
∴
Area of
Δ
A
C
E
=
1
2
×
42
×
16.8
=
705.6
2
=
352.8
Area ABCE = 468.3 + 352.8 = 821.1 m^2
In sailboat (ii),.
Area of a triangle
=
1
2
×
B
a
s
e
×
H
e
i
g
h
t
In
Δ
A
B
C
,
∠
B
=
90
∘
, base (BC) = 10.9 m and height (AB) = 19.5 m
Area of
Δ
A
B
C
=
1
2
×
10.9
×
19.5
=
212.55
2
=
106.275
m
2
In another triangular part,
Area of
Δ
D
E
F
=
1
2
×
D
F
×
E
H
=
1
2
×
23.9
×
8.6
=
205.54
2
=
102.77
m
2
Area of sailboat (ii)
=
106.275
+
102.77
=
209.045
m
2
In sailboat (iii),
Area of triangle
=
1
2
×
B
a
s
e
×
H
e
i
g
h
t
In
Δ
A
B
C
, AB = 8.9 m and BC = 3m
Area of
Δ
A
B
C
=
1
2
×
B
C
×
A
B
=
1
2
×
8.9
×
3
=
26.7
2
=
13.35
m
2
In another triangular part,
Area of
Δ
D
E
F
=
1
2
×
D
F
×
E
G
=
1
2
×
25
×
12.4
=
155
m
2
In another triangular part,
Area of
Δ
D
E
H
=
1
2
×
D
E
×
E
H
=
1
2
×
9.6
×
16.8
=
80.64
m
2
∴
Area of sailboat (iii) = 155+ 80.64
=
235.64
m
2
Answer:
235.64 m2
Step-by-step explanation:
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