FINDING AREA OF PARALLELOGRAM AND RHOMBUS WORD PROBLEMS

Problem 1 :

A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.

Solution :

In rhombus length of all sides are equal.

Perimeter of rhombus  =  160 m

Let "x" be the side length of rhombus 

4x  =  160

x  =  40 m

Area of rhombus  =  2 (Area of triangle whose sides length are 40 m, 40 m and 48 m)

s  =  (a + b + c)/2

s  =  (40+40+48)/2  =  64

  =  √s(s - a) (s - b) (s - c)

  =  √64 ⋅ (64 -  40) (64 - 40) (64 - 48)

  =  √64 ⋅ 24 ⋅ 24 ⋅ 16

  =  768 m²

Area of rhombus  =  2(768)

=  1536 m²

Problem 2 :

The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of one of the diagonal is 42 m. Find the area of parallelogram

Solution :

Area of parallelogram  =  2(Area of triangle whose sides are 34 m, 20 m and 42 m)

s  =  (a + b + c)/2

s  =  (34+20+42)/2  =  48

  =  √s(s - a) (s - b) (s - c)

  =  √48 ⋅ (48 -  34) (48 - 20) (48 - 42)

  =  √48 ⋅ 14 ⋅ 28 ⋅ 6

  =  336 m²

Area of rhombus  =  2(336)

=  672 m²

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