Question

a kite in the shape of square with a diagonal 32 cm and an isosceles triangle of base 8 cm and side 6 cm is to be made up of three different shade as shown in figure how much paper of each shade has been used in it​

Answer 1

Let the kite is made with square ABCD

& an isosceles ∆DEF.

Given, sides of a ∆DEF are DE=DF= 6cm & EF= 8cm

& Diagonal of a square ABCD= 32cm

We know that,

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

OA=OB=OC=OD=32/2=16cm

AO perpendicular BC & DO perpendicular BC

Area of region I = Area of ∆ABC= ½×BC×OA

[Area of right Triangle=1/2× base height]

Area of region I= ½×32×16=256cm²

Similarly area of region II = 256cm²

For the III section,

Now, in ∆DEF

let the sides a=6cm,b= 6cm & c=8cm

Semi perimeter of triangle,s = (6 + 6 + 8)/2 cm = 10cm

Using heron’s formula,

Area of the III triangular piece = √s (s-a) (s-b) (s-c)

= √10(10 – 6) (10 – 6) (10 – 8)

= √10 × 4 × 4 × 2

=√2×5×4×4×2

=√2×2×4×4×5

=2×4√5=8√5

= 8×2.24=17.92cm²

[√5= 2.24...]

Hence, area of paper of I colour used in making kite= 256cm²

Area of paper of II colour used in making kite= 256cm²

And area of paper of III colour used in making kite= 17.92cm²

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Answer 2

Step-by-step explanation:

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?

For I and II section:

For calculating the area of the square, Let the length of side = x cm

Each Interior Angle of square = 90ºPythagoras Theorem: Square of Hypotenuse equals to the sum of squares of other two sides

Now by Pythagoras theorem,x2 + x2 = 32 x 32

2 x2 = 32 x 32

x2 = 16 x 32 = 512 cm2

Area of Square = (side)2

And this will be the area of Square.

Area of square = 512 cm2

Area of section I = Area of section II = 1/2 Area of squareNow, we need half of this area,So half of the area of square = 256 cm2

For the III section

Length of the sides of triangle = 6cm, 6cm and 8cm

Perimeter of triangle = 6 + 6 + 8 = 20 cm

Semi-Perimeter of Triangle, s = 10 cmUsing Heron’s formula,

Area of the III triangular piece =

where, s = semiperimeter and a, b, and c are the sides of the triangle

Area of Triangle =

=

Area of Triangle = 8√5 cm2

= 17.92 cm2