Q. 234.1( 35 Votes )

Radha made a picture of an airplane with colored paper as shown in Figure. Find the total area of the paper used.

Answer :

To Find: Total area of the paper used.

Given: Picture of the airplane


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Area of Rectangle = length × breadth


Area of trapezium = 1/2 × height × sum of parallel sides


Area of right-angled triangle = 1/2 base × height


Diagram:



Explanation:


As we can see the airplane is divided into 5 parts. Let us calculate the area of each part.


Part I.


This is a triangle with sides,


a = 5 cm,


b = 5 cm, and


c = 1 cm







Part II.


Now, this is a rectangle with,


Length = 1 cm


Breadth = 6.5 cm


Area of rectangle = 1 × 6.5 cm2 = 6.5 cm2


Part III.


Diagram:



In Δ AED, applying Pythagoras theorem, we get,


(Hypotenuse)2 = (Base)2 + (Perpendicular)2


(1)2 = (1/2)2 + (height)2




This part is a trapezium with,


Sum of parallel sides = (1 + 2) cm = 3 cm





Part IV.


This is a right-angled triangle with,


Base = 1.5 cm


Height = 6 cm


Area = (1/2 × 1.5 × 6) cm2


Area = 4.5 cm2


Part V.


This is a right-angled triangle with,


Base = 1.5 cm


Height = 6 cm


Area = (1/2 × 1.5 × 6) cm2


Area = 4.5 cm2


Total Area = Area I + Area II + Area III + Area IV + Area V



Let us put the value of √11 = 3.31 and √3 = 1.73, we have now,


Total Area = 0.75 × 3.31 + 6.5 + 0.75 × 1.73 + 4.5 + 4.5


Total Area = 2.49 + 6.5 + 1.3 + 9


Total Area = 19.29 cm2 = 19.3 cm2


Hence, total area of paper needed is 19.3 cm2.


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