Kite

John has a kite, which is diamond-shaped (rhombus). Its diagonals are 60 cm long and 90 cm long. Calculate:

a) the diamond side
b) how much paper does John need to make a kite if he needs paper on both sides and needs 5% of the paper for bending?

Final Answer:

a =  54.0833 cm
S =  5670 cm²

Step-by-step explanation:

$$\begin{gathered} d_1=60\text{cm} \\ {d}_2=90\text{cm} \\ {a}^2=(d_1/2{)}^2+(d_2/2{)}^2 \\ a=\sqrt{(d_1/2{)}^2+(d_2/2{)}^2}=\sqrt{(60/2{)}^2+(90/2{)}^2}=15\sqrt{13}=54.0833\text{cm} \end{gathered}$$

$$\begin{gathered} q=100\%+5\%=1+\frac{5}{100}=1.05 \\ {S}_1=\frac{d_1\cdot d_2}{2}=\frac{60\cdot 90}{2}=2700{\text{cm}}^2 \\ S=2\cdot q\cdot S_1=2\cdot 1.05\cdot 2700=5670{\text{cm}}^2 \end{gathered}$$

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