`Delta ABC ~ Delta DEF`. BC = 3cm, EF = 4cm and area of `Delta ABC = 54 cm^(2)`. Determine the area of `Delta DEF`.

(ix) AD, BE and CF are the three medians of Delta ABC and intersect at G. The area of the Delta ABC is 36 Sq. cm. Find (a) the area of Delta AGB and (b) the area of the quadrilateral BDGF.

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

In Delta ABC , right angle is at B,AB = 5cm and angle ACB =30^(@) Determine the lengths of the sides BC and AC.

(iv) The centroid of the Delta ABC is G, If the area of the Delta GBC be 12 Sq. cm, the area of the Delta ABC is

ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, BP = 3cm, AQ = 1.5 cm and CQ = 4.5 cm, prove that area of Delta APQ = (1)/(16) ( area of Delta ABC ).

In Delta ABC, AB=6sqrt(3)cm, AC= 12cm and BC = 6 cm. Then the value of /_B will be

Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

Construct a triangle ABC of sides AB = 6 cm , BC = 9 cm and angleABC=55^(@) .

D, E, F are mid points of sides BC, CA, AB of Delta ABC . Find the ratio of areas of Delta DEF and Delta ABC .