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made a picture of an aeroplane with coloured paper as shown in figure. Find the total area of the paper used.
image
Answer :

For part I :
It is a triangle with sides 5 cm, 5 cm and 1 cm.

Thus, We know that,

s=a+b+c2
? s=5+5+12=112cm

Now, Area of part I triangle
= 112(112?5)(112?5)(112?1)
(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])

= 112×12×12×92
= 3411cm2
= 34×3.31cm2 = 3 × 0.829cm2 = 2.487cm2(approx)

For part II :

It is a rectangle with sides 6.5 cm and 1 cm

? Area of part II = 6.5 × 1
(Since, Area of rectangle = Lenght × Breadth)

= 6.5cm2

For part III :

It is a trapezium ABCD.

image

?EBC is an equilateral with side 1 cm.
? Area of ?EBC = 12 × EB × CF = 34×12
(Since, Area of triangle = frac12 × Base × Height and Area of equilateral triangle = frac34×(side)2)

? 12 × 1 × CF = 34
? CF = 32cm

Now, Area of trapezium
= 12 × Sum of parallel sides × Height
= 12 × (AB + CD) × CF
= 12 × (2 + 1) × 32
= 34 × 3
= 3 × 0.433
= 1.299 cm2

Therefore, Area of part III is 1.299 cm2

For part IV & V :

Both the parts IV and V are the same.

? it is a right triangle with sides 6 cm and 1.5 cm.

Area of part IV & V = 12 × 1.5 × 6 = 92 = 4.5 cm2

So, we get,

Total area of paper used = Area of (I + II + III + IV + V)
= (2.487 + 6.5 + 1.299 + 4.5 + 4.5)cm2
= 19.286cm2
= 19.3cm2(approx.)