A field is divided into four regions. What is the area of the field

A field is divided into four regions as shown in the given figure. What is the area of the field in square metres?

  1. 6 + 3√5/4
  2. 5 + 3√3/2
  3. 9 + 3√15/4
  4. 7 + 2√2

Answer

The field has one triangle on the left side, one right triangle, one rectangle and one quadrilateral.

Area of rectangle = 2 × 1 = 2

Area of right triangle = 1/2 × 2 × 3 = 3

Divide the quadrilateral into two parts - triangle and rectangle.

Area of rectangle = 2 × 1 = 2

Area of triangle = 1/2 × 2 × 2 = 2

Total Area = 9 m2 + area of the left triangle, which means area of the field is greater than 9. The only option for this is C.

Area of the triangle on the left side using Heron's formula

s = (3+2+4)/2 = 9/2

Area = √[(9/2)(3/2)(5/2)(1/2)] = 3√15/4

The correct option is C.