"Question 7 A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?
Class 9 - Math - Heron's Formula Page 207"
Attachments:
Answers
Answered by
313
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.....
=========================================
Attachments:
Answered by
276
heyy mate.....
here's your answer.
here's your answer.
Attachments:
Similar questions
Geography,
8 months ago
Math,
8 months ago
Physics,
1 year ago
Social Sciences,
1 year ago
Science,
1 year ago
Social Sciences,
1 year ago
Chinese,
1 year ago