Question

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

• A. $Area\left(\Delta ABD\right)=256c{m}^2,Area\left(\Delta BCD\right)=256c{m}^2,Area\left(\Delta CEF\right)=17.92c{m}^2$
• B. $Area\left(\Delta ABD\right)=258c{m}^2,Area\left(\Delta BCD\right)=258c{m}^2,Area\left(\Delta CEF\right)=17.92c{m}^2$
• C. $Area\left(\Delta ABD\right)=256c{m}^2,Area\left(\Delta BCD\right)=256c{m}^2,Area\left(\Delta CEF\right)=18c{m}^2$
• D. None of these.

Answer 1

The correct option is A

$Area\left(\Delta ABD\right)=256c{m}^2,Area\left(\Delta BCD\right)=256c{m}^2,Area\left(\Delta CEF\right)=17.92c{m}^2$

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.

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

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

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