NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 2

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Q-3 Radha made a picture of an airplane with colored paper as shown in figure. Find the total area of the paper used.

Picture of an Airplane

Solution:

We can divide the airplane into the separate quadrilaterals and triangles. Let’s find each of their areas

For triangle (i)

Isolated Top Triangle from the Airplane

This triangle is an isosceles triangle, therefore its perimeter and semi-perimeter

By using heroes formula, area of the triangle

  • (approx.)

For quadrilateral (ii)

Rectangle in Middle Part of Aircraft

Area of Rectangle

For quadrilateral (iii)

Trapezium at Tail of Aircraft

This quadrilateral is a trapezium. To find the area we need to first find its height. =

  • Perpendicular height of parallelogram

  • Area=area of parallelogram+ area of equilateral triangle

For triangle (IV) = triangle (v)

We know

  • (2 triangle)

Therefore, total area of the paper used