Activity 6
See the problem
42 sq. cm
14 sq. cm
С
A
M
28 sq. cm
B.
The ratio of areas of triangles lies above the diagonal AC of the quadrilateral on the
figure.
= 42:14
= 3:1
If MC= 7 cm, then
AM
cm
9632
What is the area of triangle AMB?
If DM = 5 cm, then
BM
cm
Answers
Given :-
- The ratio of area triangle lies above the diagonal AC of the quadrilateral on the figure is 42 : 14 = 3 : 1.
- MC = 7 cm .
- DM = 5 cm .
- Area CMB = 28 cm² .
To Find :-
- AM = ?
- Area of ∆AMB = ?
- BM = ?
Answer :-
→ Area ∆AMD : Area ∆AMC = 42 : 14 : 3 : 1
→ (1/2) * AM * MD * sin θ : (1/2) * MC * MD * sin (180 - θ) = 3 : 1
→ AM * sin θ : MC * sin θ = 3 : 1
→ AM : MC = 3 : 1
→ AM/MC = 3/1
→ AM/7 = 3/1
→ AM = 21 cm (Ans.)
similarly,
→ Area AMB : Area CMB = AM : CM
→ Area AMB : 28 = 21 : 7
→ Area AMB / 28 = 3/1
→ Area AMB = 28 * 3
→ Area AMB = 84 cm² .
similarly,
→ Area DMC : Area BMC = DM : BM
→ 14 : 28 = 5 : BM
→ (1/2) = 5/BM
→ BM = 10 cm (Ans.)
Conclusion :- Ratio of areas of ∆'s lies on either side of a straight line is equal to ratio of their base .
Learn more :-
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