# Radha made a picture of an aeroplane with coloured paper as shown in the figure. Find the total area of the paper used.

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

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For the triangle marked I : a = 5 cm, b = 5 cm, c = 1 cm

∴ s = (a +b + c)/ 2 =  (5 +5+ 1) /2 cm =  11 / 2 cm  =5.5 cm   For the rectangle marked II :

Length = 6.5 cm, Breadth = 1 cm

Area of the rectangle = 6.5 × 1 cm2 = 6.5 cm2 For the trapezium marked III :

Draw AF || DC and AE ⊥ BC.

AD = FC = 1 cm, DC = AF = 1 cm

∴ BF = BC – FC = (2 – 1) cm = 1 cm

Hence, ∆ABF is equilateral.

Also, E is the mid-point of BF.

∴ BE = 1/ 2 cm = 0.5 cm

Also, AB2 = AE2 + BE2 [Pythagoras theorem]

⇒ AE2 = 12 – (0.5)2 = 0.75

⇒ AE = 0.9 cm (approx.)

Area of the trapezium = 1/ 2 (sum of the parallel sides) × distance between them.

= 1/ 2 × (BC + AD) × AE = 1/ 2 × (2 + 1) × 0.9 cm2 = 1.4 cm2

For the triangle marked IV :

It is a right-triangle

∴ Area of the triangle = 1/ 2 × base × height

= 1/ 2 × 6 × 1.5 cm cm2 = 4.5 cm2

For the triangle marked V :

This triangle is congruent to the triangle marked IV.

Hence, area of the triangle = 4.5 cm2

Total area of the paper used = (2.5 + 6.5 + 1.4 + 4.5 + 4.5) cm2