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

# A kite is in the shape of a square with a diagonal of    and an isosceles triangle of base    and sides    each is to be made of three different shades as shown in the figure. ____ paper of each shade has been used in it?

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### Solution:

Let us find the area of part 1 first
(i) Area of part 1
Let us assume that the triangle  in different orientation as follows

We know that the all sides of square are equal so, let us assume that

We are given that the length of diagonal as    so, we have

The Pythagoras theorem is given as  .
By using the above theorem to triangle    we get,

By substituting the required values we get

Let us assume that the area of part 1 as   .
We know that the formula of area of triangle as

By using the above formula to  we get,

By substituting the required values in above equation we get

Therefore the area of part 1 is   Now, let us solve the second part.
(i) Area of part 2
Let us assume that the area of part 2 as
We know that the diagonal of a square divides the square into two triangles of same area that is

Therefore the area of part 2 is  .
(iii) Area of part 3
Let us take the triangle    and draw the height as shown below.

We are given that the dimensions of each triangle are  .
So, from the triangle    we have,

We know that the altitude of isosceles triangle will be the median
So, the point ‘H’ is mid – point of ‘DE’
So, we can the length of ‘HE’ as

The Pythagoras theorem is given as,  .
By using the above theorem to triangle    we get,

By substituting the required values we get

We know that the formula of area of triangle as

By using the above formula to  as  ,

By substituting the required values in above equation we get

Therefore the area of third part is   .

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 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

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