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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? - CBSE Class 9 - Mathematics

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Question

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?

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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APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 12: Heron's Formula
Ex. 12.20 | Q: 7 | Page no. 207

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Solution 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? Concept: Application of Heron’S Formula in Finding Areas of Quadrilaterals.
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