find the area that needs to be added to the area of triangle ADB so that it becomes equal to the area of triangle ABC
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Find the approximate value of m if n=4 and so that the area of triangle ABC is equal to the area of trapezoid BCDO.
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Answer
Correct option is
B
2.88
Area △ABC=
2
1
[A
x
(B
y
−C
y
)+B
x
(C
y
−A
y
)+C
x
(A
y
−B
y
)]
=
2
1
[0(m−m)+0(m−8)+n(8−m)]
=
2
8n−mn
Area BCDO =
2
1
(BC+OD)×BO
=
2
1
(
(m−m)
2
+(n−0)
2
+
(6−0)
2
+(0−0)
2
)×m
=
2
1
(n+6)m=
2
(n+6)m
Now, ar △ABC = ar trap BCDO
⇒
2
8n−mn
=
2
mn+6m
⇒8n−mn=mn+6m
⇒8n=2mn+6m=2m(n+3)=8n⇒m=
n+3
4n
Put the value of n
m=
7
16
=2.88
Answer:
As median divides the triangle into two triangles of equal area, area of triangle ABC will be 40 cm^2.