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. 12.17. How much paper of each shade has been used in it?
50 cm
20 cm​

Answer 1

Answer:

$area \: of \: shade \: 1 = 25 {6cm}^{2} \\ area \: of \: shade \: 2 = 256c {m}^{2} \\ area \: of \: shade \: 3 = 17.92 {cm}^{2}$

Step-by-step explanation:

Since Diagonals Of Square Bisect It Into Two Equal Traiangles:-

Therefore Area Of Shade 1 = Area of Shade 2

Also Diagonals Bisect Each other:-

Area Of Shade 1/2 :-

$area \: of \: shade \: 1 \: = \frac{1}{2} \times base \times height \\ = ) \frac{1}{2} \times 16 \times 32 \\ = )16 \times 16 \\ = )216 {cm}^{2} \\ area \: of \: shade \: 1 = 216 {cm}^{2} = area \: of \: shade \: 2$

Area of Shade 3:-

$s = \frac{perimeter}{2} \\ = ) \frac{8 + 6 + 6}{2} \\ = ) \frac{20}{2} \\ = )10cm \\ area \: of \: shade \: 3 \: b y \: herons \: formula = ) \\ = ) \sqrt{s(s - a)(s - b)(s - c)} \\ = ) \sqrt{10(10 - 6)(10 - 6)(10 - 8) } \\ = ) \sqrt{10 \times 4 \times 4 \times 2} \\ = ) \sqrt{2 \times 5 \times 4 \times 4 \times 2} \\ = )2 \times 4 \sqrt{5} \\ = ) 8\sqrt{5} \\ = )17.92 \: {cm}^{2}$

Hope it helped