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Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.
"
Given :
The figure of the aeroplane made with coloured paper is given.
To find :
We have to find the total area of the colour paper used.
Solution :
The total area of the paper used $= part I + part II + part III + part IV + part V$
Part I :
It is an isosceles triangle with sides $a = 1\ cm, b = 5\ cm, c = 5\ cm$.
Semi perimeter, $S = \frac{a+ b + c}{2}$
$S = \frac{1+ 5 + 5}{2}$
$S= \frac{11}{2}$
$S = 5.5\ cm$
Area of triangle $= \sqrt {S (S-a)(S-b)(S-c)}$
$= \sqrt {5.5 (5.5-1)(5.5-5)(5.5-5)}$
$= \sqrt {5.5 (4.5)(0.5)(0.5)}$
$= 0.75 \sqrt{11}\ cm^2$
Part I $= 2.488\ cm^2$.
Part II :
It is a rectangle with sides $l=6.5 \ cm, b =1\ cm$
Area of rectangle $=l\times b$
$=6.5\times 1$
Part II $=6.5\ cm^2$.
Part III :
It is a trapezium.
Area of trapezium $=$ area of equilateral triangle $+$ area of parallelogram
Area of equilateral triangle $=\frac{\sqrt{3}}{4}a^2$
$=\frac{\sqrt{3}}{4}\times1$
$= \frac{\sqrt{3}}{4}$
$=0.433\ cm^2$
Area of parallelogram$=base \times height$
Height $= \sqrt{1^2 - 0.5^2} = \sqrt{0.75} = 0.866\ cm$
Area of parallelogram$=1 \times 0.866$
$= 0.866\ cm^2$
Area of trapezium $= 0.433 + 0.866$
$= 1.299\ cm^2$
Part III $= 1.299\ cm^2$.
Part IV and Part V :
These are triangles with a base of $1.5\ cm$ and a height of $6\ cm$.
Area of triangle $=\frac{1}{2} \times base \times height$
$ = \frac{1}{2} \times 1.5 \times 6$
$= 4.5\ cm^2$
Part IV $=$ Part V $= 4.5\ cm^2$.
Total area of the paper $= 2.488 + 6.5 + 1.299 + 4.5 + 4.5\ cm^2$
$ = 19.287 cm^2$
The total area of the paper is $19.287\ cm^2$.