# Q3.    Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.

The total area of the paper used will be the sum of the area of the sections I, II, III, IV, and V. i.e.,

For section I:

Here, the sides are

So, the Semi-perimeter will be:

Therefore, the area of section I will be given by Heron's Formula,

For section II:

Here the sides of the rectangle are  and

Therefore, the area of the rectangle is

For section III:

From the figure:

Drawing the parallel line AF to DC and a perpendicular line AE to BC.

...........................by construction.

...........................[  ABCD is a trapezium]

So, ADCF is a parallelogram.

Therefore,   and

Therefore,

ABF is an equilateral triangle.

Then, the area of the equilateral triangle ABF is given by:

Hence, the area of trapezium ABCD will be:

For Section IV:

Here, the base is 1.5 cm and the height is 6 cm.

Therefore, the area of the triangle is :

For section V:

The base length = 1.5cm and the height is 6cm.

Therefore, the area of the triangle will be:

Hence, the total area of the paper used will be:

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