Question

A field is in the shape of a

parallelogram. Its two adjacent sides

and one diagonal are of length 65 m,

119 m and 156 m respectively. Then

its area will be​

Answer 1

Given:

Length of diagonal = 65m

Lenght of first side = 119m

Length of second side = 156m

To Find:

The total area of the field

Solution:

Using the formula -

s = a + b + c/2

= 65 + 119 + 156/2

= 340/2

= 170

Area of Triangle = √( s ( s-a)(s-b)(s-c)

= √ 170 ( 170 - 65)(170 - 119)(170-156)

= √ 170 × 105 × 51 × 14

= √   170 × 105 × 714

= 3570

Now,

Area of Parallelogram = 2 × Area of Triangle

= 2 × 3570

= 7140

Answer: Area of the field is 7140m²