Question

What is a shape that has 3 sides of a parallelogram it is 14 cm , 9 cm and 9 camis that enough information to work out the 4 still side ???

Answer 1

Answer:

Base = 9 cm

Others sides = 12 cm and 15 cm respectively.

Also,

Area of Δ = Area of llgm

which means,

Area of Δ = Base x  Height

Area of Δ = 9 x h

∴ h = 1/9 x ( Area of Δ ) ................ (eq.1)

Now,

Area of Δ = √s(s-a)(s-b)(s-c)

where a,b,c are the sides of the triangle and s is the semi-perimeter of the triangle.

s = (a+b+c)/2

  = (9+12+15)/2

  = 36/2

  = 18 cm

Substitute the value of s,a,b,c in the formula above.

Area of Δ = √18(18-9)(18-12)(18-15)

                = √18(9)(6)(3)

                = √18 x 18 x 9

                = √18² x 3²

                = 18 x 3

                = 54 cm²

Now substitute the value of Area of Δ in eq.1

h = 1/9 x ( Area of Δ )

h = 1/9 x 54

h = 6 cm

∴ Height of the parallelogram is 6 cm

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