A Kite in the Shape of a Square with a Diagonal 32 cm and an Isosceles Triangles of Base 8 Cm and Sides 6 cm Each is to Be Made of Three Different Shades as Shown in the Given Figure. How Much Paper of Each Shade Has Been Used in It? - Mathematics

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A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

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Solution

We know that

Area of square = 1/2(diagonal)2

`"Area of the given kite "= 1/2(32 cm)^2 = 512 cm^2`

Area of 1st shade = Area of 2nd shade = 512/2 = 256 cm2

Therefore, the area of paper required in each shape is 256 cm2.

For IIIrd triangle

Semi-perimeter,

`s=(6+6+8)/2=10 cm`

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of 3rd triangle "=sqrt(10(10-6)(10-6)(10-8))`

                                `=(sqrt(10xx4xx4xx2))cm^2`

                                `=(4xx2sqrt5)cm^2`

                                `=8sqrt5 cm^2`

                                 = (8 x 2.24) cm2

                                 = 17.92 cm2

Area of paper required for IIIrd shade = 17.92 cm2

 

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Chapter 12: Heron's Formula - Exercise 12.2 [Page 207]

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NCERT Mathematics Class 9
Chapter 12 Heron's Formula
Exercise 12.2 | Q 7 | Page 207

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