Question

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 figure - 12.17. How much paper of each shade has been used in it?

Answer 1

Answer:

Area of Triangle = 17.92 cm²

Step-by-step explanation:

As the diagonals of a square bisect each other at right angle  :

So,

DM = AM = 32/2

=> 16 cm.

Area of shade I = Area of shade II = Area of  ΔABD

= 1/2 x AD × BM  = 1/2 x 32 x 16 = 256 cm²  

The area of shade III  

Area of isosceles △DEF = a/4 - (√4b² - a²)

=> 8/4 r(√4(6)² - 8²))    

=> 2(√144 - 64) = 2√80  = 85 cm²

Hence,

Area of Triangle = 17.92 cm²

Answer 2

$\huge\bf{Answer:-}$

• Let the Diagnoal = 32/2
• Hence, 32/2 is equal to 16 cm

Here,

• Area of shade part 1= Area of shade 2 is equal to Area of ΔABD

So,

• >> (1/2 x AD × BM) is equal to (1/2 x 32 x 16 = 256 cm² )

Part 3 shaded side of the triangle:-

• DEF is equal a/4 - √4b² - a²

$= \frac{8}{4} \: r \sqrt{4(6) {}^{2} - 8 {}^{2} }$

$= 2 \sqrt{180}$

$= 85cm {}^{2}$

$therefore \: 17.92cm {}^{2} Area \: of \: Triangle.$

Refer the rough diagram in the given attachment:-