Name: Area of Polygon by Triangulation
Uploaded: 2019-07-19
Duration: 11 min 5 s
Description: How can you calculate the area of polygons when you forget its formula? Simple! Break it down into shapes that you know the formula for. Watch to learn how!

Question

Suppose you have been asked to make an aeroplane from the coloured paper, as shown in figure. Find the total area of paper that you would need.

Accepted Answer

Given,

Area of $△ A B C$

Using pythagoras theorem, height of the triangle is,

$= \sqrt{10^{2} - 1^{2}} = 9.945 c m$

Since its a triangle, the area is given as,

$A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 2 \times 9.945 = 9.945 c m^{2}$

Area of part $B H K C$

Since its a rectangle, its area is given as,

$A = length \times bredth = 6.5 \times 2 = 13 c m^{2}$

Area of $H I J K$

Using pythagoras theorem the height, h of the trapezium is calculated as shown in figure above.

Since its a trapizoidal, area is given as,

$A = \frac{1}{2} \times (a + b) \times h = 2 \times \sqrt{3} + \frac{1}{2} \times 2 \times \sqrt{3} = 3 \sqrt{3} = 5.196 c m^{2}$

Area of $△ B D E$ and $△ C G F$

Area for triangle is,

$A = \frac{1}{2} \times 6 \times 1.5 = 4.5 c m^{2}$

So the total area is the sum of all the individual parts i.e.

$= 9.945 + 13 + 5.196 + 4.5 + 4.5 = 37.141 c m^{2}$

S Purkayastha Solutions for Chapter: Area of Polygons, Exercise 8: Maths in Real Life

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Area of Polygons, Exercise 8: Maths in Real Life

Questions from S Purkayastha Solutions for Chapter: Area of Polygons, Exercise 8: Maths in Real Life with Hints & Solutions

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