Areas of Parallelograms and Triangles Test - 4

The median of a triangle divides it into two triangles of different areas.

If in a triangle ABC, AD is a median, then

Area of triangle ABD = Area of triangle ACD.

Since the figure obtained by joining the mid-points of the adjacent sides of a rhombus is rectangle, then

Side of rectange = PQ = 1/2AC                    [Mid-point theorem]

=>     PQ = 1/2x 16 = 8 cm

Similarly, QR = 1/2x 12 = 6 cm

Therefore, Area of rectangle PQRS = PQ x QR = 8 x 6 = 48 cm²

The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is a rectangle with are 48 sq. cm.

Since figure obtained by joining the mid-points of the adjacent sides of a rectange is a rhombus.

Then diagonals of the rhombus PQRS are QS and PR i.e., sides of rectangle ABCD.

Therefore, QS = 8 cm and PR = 6 cm

Now, Area of rhombus PQRS = 1/2x QS x PR = 1/2x 8 x 6 = 24 cm²

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a rhombus with area 24 sq. cm.

ABCD is quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD can be either a rhombus or a rectangle or a parallelogram.

Therefore, it needs not be any of (a), (b) or (c).

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is 1 : 1.

Becasue when two parallelogram are on same base and between the same parallels, then the areas of both parallelograms are equal.

If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is 1 : 2.

Area of triangle = 1/2x Area of parallelogram

=>          Area of triangle : Area of parallelogram = 1 : 2