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 cm^{2} = 6.5 cm^{2}

**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) cm^{2}

Area = 4.5 cm^{2}

**Part V.**

This is a right-angled triangle with,

Base = 1.5 cm

Height = 6 cm

Area = (1/2 × 1.5 × 6) cm^{2}

Area = 4.5 cm^{2}

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 cm^{2} = 19.3 cm^{2}

**Hence, total area of paper needed is 19.3 cm ^{2}.**

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