ig.
Find the area of the following figures.
D
F
E
7 cm
2 cm
2.4 cm
A
B
C С
8 cm
(a)
Answers
Answer:
(i) If AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm, find EC and AC.
(ii) If AB = 13.3 cm, AC = 11.9 cm and EC = 5.1 cm, find AD.
(iii) If
AD
DB
=
4
7
and AC=6.6 cm, find AE.
(iv) If
AD
AB
=
8
15
and EC=3.5 cm, find AE.
ANSWER:
(i)
In △ ABC, it is given that DE∥BC.
Applying Thales' theorem, we get:
AD
DB
=
AE
EC
∵ AD = 3.6 cm , AB = 10 cm, AE = 4.5 cm
∴ DB = 10 - 3.6 = 6.4 cm
or,
3.6
6.4
=
4.5
EC
or, EC =
6.4×4.5
3.6
or, EC =8 cmThus, AC = AE +EC = 4.5 + 8 = 12.5 cm
(ii)
In △ABC, it is given that DE ∥BC.Applying Thales' Theorem, we get:
AD
DB
=
AE
EC
Adding 1 to both sides, we get:
AD
DB
+1 =
AE
EC
+1⇒
AB
DB
=
AC
EC
⇒
13.3
DB
=
11.9
5.1
⇒DB =
13.3×5.1
11.9
= 5.7 cm
Therefore, AD = AB - DB = 13.5 - 5.7 = 7.6 cm
(iii)
In △ABC, it is given that DE∥BC.Applying Thales' theorem, we get:
AD
DB
=
AE
EC
⇒
4
7
=
AE
EC
Adding 1 to both the sides, we get:
11
7
=
AC
EC
⇒EC =
6.6×7
11
= 4.2 cmTherefore, AE = AC -EC= 6.6-4.2 = 2.4 cm
(iv)
In △ABC, it is given that DE∥BC.Applying Thales' theorem, we get:
AD
AB
=
AE
AC
⇒
8
15
=
AE
AE + EC
⇒
8
15
=
AE
AE + 3.5
⇒8AE + 28 = 15AE⇒7AE = 28⇒AE = 4 cm