Question

Smaller diagonal of rhombus is equal to the length of its sides.If length of each side is 4 cm,what is the areaof an equilateral triangle with side equal to the diagonal of the rhombus?

Answer 1

Answer:

diagonal of rhombus=side of equilateral triangle

Side=4cm

Area of triangle= √3/4*side ^2 ( because it is equilateral triangle)

Answer is 4√3 sq cm

Answer 2

Answer:

20.78

Step-by-step explanation:

AB = BD = 4 cm

ΔABD is an equilateral triangle

 Ar (ΔABD) = √3 (side)2/4

Ar (ΔABD) = 4√3

 Ar (rhombus ABCD) = 2 [Ar (ΔABD)]

Ar (rhombus ABCD) = 8√3

Ar (rhombus ABCD) = ( 1/2) × AC ×BD

(1/2) × AC × BD = 8√3

AC = (8√3 × 2)/4 = 4√3

AC is the side of new equilateral Δ

Area of new triangle = [√3 × (4√3)2]/4

Required area = 12√3 cm^2