9th Class
Mathematics
Geometry
Question Bank
Geometry
question_answer
In a triangle ABC, D and E are the midpoints of AB and AC. If the area of AABC = 60 sq cm. then the area of the A ADE is equal to
A) 15 sq cm
B) 20 sq cm
C) 25 sq cm
D) 30 sq cm
Correct Answer:
A
Solution :
Referring figure, \[DE=\frac{1}{2}BC\] and \[AP=\frac{1}{2}AQ\] Given, Area of \[\Delta \,ABC=60\,c{{m}^{2}}\] or \[\frac{1}{2}\times BC\times AQ=60\] or \[BC\times AQ=120\] \[\therefore \] Area of \[\Delta \,ADE=\frac{1}{2}\,DE\times AP\] \[=\frac{1}{2}\times \frac{1}{2}BC\times \frac{1}{2}AQ=\frac{1}{8}BC\times AQ\] \[=\frac{1}{8}=120=15\,sq.\,cm.\]