Radha made a picture of an aero plane with colored paper as shown in Fig 12.15. Find the total area of the paper used.

Question

Philoid · Accepted Answer

The figure of the questions is:

Sides of triangular section I = 5cm, 1cm and 5cm

Perimeter of the triangular section I = 5 + 5 + 1 = 11cm

Semi perimeter, s = = = 5.5cm

We use Heron’s formula to find the area of the section I,

Area of Section I =

=

= $\sqrt{6.1875}$ cm²

Area of Section I = 2.48 cm² (approx.) ~ 2.5 cm²

Length of the sides of the rectangle of section I = 6.5cm and 1 cm

Area of section II = 6.5×1 = 6.5cm²

Section III is an isosceles trapezium which is divided into three equilateral triangles each with side of 1cm each.

Now, Area of an equilateral triangle is $\frac{\sqrt{3}}{4}\times side^{2}$

Thus, area of one equilateral triangle is $\frac{\sqrt{3}}{4}\times 1^{2} = 0.43 cm^{2}$

Therefore, the area of trapezium = 3 $\times$ 0.43cm²= 1.3 cm²

Section IV and V are congruent right angled triangles with height 1.5cm and base 6cm.

And, area of a right triangle = $\frac{1}{2}\times Base \times height = \frac{1}{2}\times1.6\times 6 = 4.8 cm^{2}$

Area of region IV and V = 2 $\times$ 4.8 cm²= 9.6 cm²

^{Thus, total area is 2.5 + 6.5 + 9.6 + 1.3 = 19.9 sq cm}^{~ 20 sq cm}