A field is in the shape of a rhombus. Its perimeter is 584…

A field is in the shape of a rhombus. Its perimeter is 584 m, and the length of one of its diagonals is 220 m. What is the area (in m²) of the field?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 21,120.

Perimeter = 584 = 4a [a = side]

⇒ Side = $584 \over 4$ = 146 m

Diagonal(DB) = 220 m

In △DOC

⇒ DC² = DO² + OC²

⇒ (146)² = (110)² + OC²

⇒ OC² = (146)² - (110)²

⇒ OC² = (146 + 110)(146 - 110)

⇒ OC² = 256 × 36

⇒ OC = 96

⇒ AC = 2 × OC = 192

Area of the rhombus = ${1\over2}\times AC \times DB$

⇒ ${1\over2}\times 192\times 220$ = 21120 m²

SSC Selection Post 2022 PYQ — Question 58