Question

A kite in the shape of a square with each diagonal 32 cm and having a tail in the shape of an isosceles triangle of base 8 cm and each side 6 cm, is made of three different shades as shown in the figure. How much paper of each shade has been used in it?
[Given $\sqrt{5}=2.24$ ]

Answer 1

One shaded portion is $\Delta ABD$.\)

$=(\frac{1}{2}\times BD\times AO)=(\frac{1}{2}\times 32\times 16)c{m}^2$

$=256c{m}^2$

Second shaded portion is $\Delta BCD$

$ar\left(\Delta BCD\right)=ar\left(\Delta ABD\right)=256c{m}^2$

Third shaded portion is CEF in which CE = CF = 6cm and EF = 8cm.

$\therefore s=\frac{1}{2}(6+6+8)=10,(s-a)=4,(s-b)=4,(s-c)=2$

$\therefore ar\left(\Delta CEF\right)=\sqrt{10\times 4\times 4\times 2}=8\sqrt{5}$

$=(8\times 2.24)c{m}^2=17.92c{m}^2$