The perimeter of a rhombus is 40 cm, its measure of an angle is 60 degree, then its area is?
Answer & explanation
Correct answer: option 3
\(\angle\)A = 60° ⇒ \(\angle\)C = 60°
\(\angle\)B = \(\angle\)D = \(\frac{360° - 120°}{2}\) = 120°
\(\angle\)ABD = \(\angle\)ADB = 60°
ΔABD is equilateral Δ ; [ side = \(\frac{40}{4}\) = 10 cm]
Area of rhombus = 2 × area of ΔABD
= 2 × \(\frac{\sqrt {3}}{4}\)(10)2
= 50\(\sqrt {3}\)cm2