Question

a triangle and parallelogram have the same base the same area if the sides of the triangle are 26 28 cm and 30 cm and the parallelogram stands on the base of 28 cm find the height of the parallelogram​

Answer 1

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Answer 2

Answer:

Height of parallelogram = 12 cm

Step-by-step explanation:

Formula : Area of parallelogram

= Base × Height

Given that,

Area of parallelogram = Area of triangle

Base * Height = Area of triangle

28 * Height = Area of triangle

Height = (1/28)* Area of triangle

first we have to find triangle :

Area of triangle = √s(s-a)(s-b)(s-c)

Here, s is the semi-perimeter,

and a, b, c are sides of the triangle.

Here, a = 26 , b = 28 , c= 30

s = (a+b+c)/2 = (26+28+30)/2 = 84/2

s = 42 m

Area of triangle

= √42(42-26)(42-28)(42-30) cm^2

= √42(16)(14)(12)

= √(14*3)(14)(12)(16)

= √(14*14)(12*3)(16)

= √(14)^2*(6)^2*(4)^2

= 14*6*4

= 336 cm^2

Thus, Area of triangle = 336 cm^2

Now,

Height = (1/28)*Area of triangle

Height = (1/28)*336

Height = 12 cm

Therefore, the height of the parallelogram is 12 cm.