Question

draw a parallelogram whose two adjacent sides are 5 cm and 7 cm and the angle include between them is 60° draw a triangle equal in area to this parallelogram ( construct by figure)​

Answer 1

Answer:

Given, ABCD is a parallelogram having AB=5 cm,BC=3.5 cm and one of the diagonal AC=6.5 cm.

We know that the diagonal of a parallelogram divides it into two triangles of equal area.

Therefore, in triangle ABC, by heron's formula, we have a=5 cm,b=3.5 cm and c=6.5 cm

⇒ semi-perimeter of triangle ABC,s=

2

a+b+c

=

2

5+3.5+6.5

=7.5 cm

∴ Area of triangle ABC=

s(s−a)(s−b)(s−c)

=

7.5(7.5−5)(7.5−3.5)(7.5−6.5)

=5

3

cm

2

⇒ Area of parallelogram ABCD=2×area of triangle ABC=2×5

3

cm

2

=10

3

cm

2