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

Answer:

Step-by-step explanation:

diagonal  = 32 cm

Area of square = $\dfrac{d^{2}}{2}$

                        $=\dfrac{32*32}{2}\\\\=512 \ cm^{2}$

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

$s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}$

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)