We know that, all the sides of a square are always equal
i.e., AB = BC = CD = DA
In ΔACD, AC=44cm, ∠D=90∘
Using Pythagoras theorem in ΔACD,
AC2=AD2+DC2
⇒ 442=AD2+AD2 [∵ DC=AD]
⇒ 2AD2=44×44
⇒ AD2=22×44⇒AD=√22×44
[taking positive square root because length is always positive]
⇒ AD=√2×11×4×11
⇒ AD=22√2cm
So, AB = BC = CD = DA = 22√2cm
∴ Area of square ABCD =Side×Side=22√2×22√2=968 cm2
∴ Area of the red portion =9684=242cm2
[since, area of square is divided into four parts]
Now, area of the green portion =9684=242cm2
Area of the yellow portion =9682=484cm2
In ΔPCQ, side PC = a = 20cm, CQ = b = 20cm and PQ = c = 14cm
s=a+b+c2=20+20+142=542=27 cm
∴ Area of ΔPCQ=√s(s−a)(s−b)(s−c) [by Heron’s formula]
=√27(27−20)(27−20)(27−14)
=√27×7×7×13=√3×3×3×7×7×13
=21√39=21×6.24=131.04cm2
∴ Total area of the green portion = 242 + 131.04 = 373.04 cm2
Hence, the paper required for each shade to make a kite is red paper 242 cm2,
yellow paper 484 cm2 and green paper 373.04 cm2.