Question

one of the diagonals of a parallelogram whose sides are 50 cm, and 14 cm is of length 48 cm. find the area of the parallelogram.​
PLEASE EXPLAIN THIS IN BRIEF.

Answer 1

Answer:

672 sq cm

Step-by-step explanation:

we know that area of parallelogram is base x height

here we can take either side as base but height is not known. we further know that area of a parallelogram is twice the area of triangles made using one of its diagonals.

we split the parallelogram in two triangles using diagonal of 48 cm

the sides of a triangle are 50 cm, 14 cm and 48 cm

using herons formula, we will find the area of triangle

s= (a+b+c)/2

= (50+14+48)/2

= 112/2

= 56 cm

area of triangle = √s(s-a)(s-b)(s-c)

√56*6*42*8

=√ 7*8*6*7*6*8

= √7*7*6*6*8*8

= 7*6*8

= 336 sqcm

so area of parallelogram = 2x area of triangle

= 2*336

= 672 sq cm