A kite is in the shape of a rhombus with a diagonal 48cm nad an equilateral triangle of 5cm - Maths - Triangles

Question

A kite is in the shape of a rhombus with a diagonal 48cm nad an
equilateral triangle of 5cm It is to me made of five different
colors Find the area of paper of each color used ( I did not get
any other figure, so please refer to the figure acordingly All five
triangles have to be made of 5 different colors Use root 3 = 1 73
)

Manbar Singh · Accepted Answer

Let ABCD is a rhombus in which AC and BD are the diagonals that intersect each other at O
Let AC = 48 cmWe know that diagonals of a rhombus bisect each other at right angle, thenOA = OC = 24 cm; OB = OD
Also, ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
Now, we have CEF as an equilateral ∆ in which CF = FE = CE = 5 cm
Also each angle of an equilateral ∆ is 60°, then∠ECF = 60°
Since BE and DF are straight lines that intersect at C, then∠BCD = ∠ECF = 60°   Vertically opposite anglesWe know that a diagonal of a rhombus bisect each of the opposite angle, then∠OCD = ∠OCB = 12∠BCD = 30°
Now, in ∆BOC, we havetan 30° = perpendicularbase⇒13 = OBOC⇒OB = OC3 = 243 = 2433 = 83 cmNow, OD = OB = 83 cmNow, ar∆BOC = 12×OB×OC = 12×83×24 = 963 cm2
We know that diagonals of a rhombus divides it into 4 congruent ∆'s of equal areas
So, ar∆AOB = ar∆BOC = ar∆COD = ar∆DOA = 963cm2 = 166
08 cm2Now, side of equilateral ∆CEF ,s = 5 cmar∆CEF = 34s2 =3452 = 2534 = 10
8125 cm2 Hence, ar∆AOB = ar∆BOC = ar∆COD = ar∆DOA =166
08 cm2and ar∆CEF =10 8125 cm2