Question

7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 8.17. How much paper of each shade has been used in it?​

Answer 1

Explanation:

diagonal = 32 cm

Area of square =
`(d^(2))/(2)`

`=(32*32)/(2)\\\\=512 \ cm^(2)`

Diagonal separate the square into two equal triangles.

Area of upper triangle that is shaded black = area of lower triangle = 512/2

= 256 cm²

Isosceles triangle:

a = 6 cm ; b = 6 cm c = 8cm

`s = (a+b+c)/(2)\\\\=(6+6+8)/(2)\\\\=(20)/(2)\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = √(s*(s-a)(s-b)(s-c))\\\\=√(10*4*4*2)\\\\=√(2 * 2 * 4 * 4 * 5)\\\\=4*2√(5)\\\\=8√(5)\\\\=8*2.24\\\\=17.92 \ cm^(2)`

Area of black shade paper = 256 + 17.92 = 273.92 cm²

Area of white shade paper = 256 cm²

Area of the isosceles triangle = s(s-a)(s-b)(s-c)