2017 · Q90
A field is divided into four regions as shown in the given figure. What is the area of the field in square metres ?
Elementary MathematicsMensuration
- A6 + 3/4√(5)
- B5 + 3/2√(3)
- C9 + 3/4√(15)
- D7 + 2√(2)
Explanation
From the figure the four regions are: ΔABD with sides 2, 3, 4; right ΔCDF; rectangle BECF; and quadrilateral EFGH. By Heron's formula with s = 9/2, area(ΔABD) = √[(9/2)(5/2)(3/2)(1/2)] = 3√15/4. The others are ½·3·2 = 3, 2·1 = 2, and ½·4·2 = 4. Total = 9 + 3√15/4: option C.