Question

ABCD is a quadrilateral whose sides are 40m,42m,30m,32m . Then find the area of quadrilateral...

Answer 1

Given the sides a, b, c and d of a quadrilateral we can use the formulae below to get the area.

A = √(s- a) (s - b) (s - c) (s - d)

s = (a + b + c + d) /2

s = (40 + 42 + 32 +30) / 2 = 144/2 = 72

Substituting in the formula :

A =√(72 - 40)(72 - 42)(72 - 32)(72 - 30)

A = √(32 × 30 × 42 × 40) = √1612800

A =√1612800 =1269.96m²

Answer 2

Solution :-

Ancient Indian Mathematician (CE 598 - 665) Brahmagupta gave the following formula for finding the area of a quadrilateral, which does not require the angle measurement. Only length of four sides is sufficient. 

Area = √(s - a)(s - b)(s - c)(s - d)

s = (a + b + c + d)/2

a, b, c and d are four sides respectively.

⇒ (40 + 42 + 30 + 32)/2

⇒ 144/2

s = 72 m 

Area = √(72 - 40)(72 - 42)(72 - 30)(72 - 32)

⇒ √32*30*42*40 

⇒ √1612800

⇒ Area = 1269.96 m²

Answer.