256

The perimeter of a triangle is equal to the sum of its three sides it is denoted by 2S. 2s=(a+b+c) s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

The formula given by Heron about the area of a triangle is known as Heron's formula.

According to this formula area of a triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle and s is a semi perimeter.

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily . Heron's formula is generally used for calculating area of scalene triangle. ________________ ____________________

Solution:

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

Hope this will help you.....