meera is a student of class 9 . she want to fill green colour in triangle of the given rangoli . she known that the one triangle at the top is an equivalent triangle each side having 5 cm , remaining 4 and the iscoles traingle side having 4 cm and base 6 cm . question and answer. 1. which mathematical concept meera can use to find the area of all traingle . 2. find the cost of green colour used if rate of the colouring is 50 paise per cm . 3 . what value of woman are depicted by drawing the rangoli .
Answers
Given : one triangle at the top is an equilateral triangle each side having 5 cm ,
Remaining 4 are the isosceles triangle side having 4 cm and base 6 cm .
To Find : 1. which mathematical concept Meera can use to find the area of all triangle
2. find the cost of green colour used if rate of the colouring is 50 paise per cm²
Solution:
mathematical concept to find the area of all triangle can be used :
Heron' formula
Sides of triangle a , b , c
s = semi perimeter = (a + b + c)/2
Area = √s(s - a)(s - b)(s-c)
Equilateral triangle each side having 5 cm ,
a = b = c = 5
s = 15/2
Area = √(15/2)(15/2 - 5)(15/2 - 5)(15/2 - 5)
= (1/4) √(5 * 3)(5)(5)(5)
= 25√3 / 4 cm²
= 10.825 cm²
Also for Equilateral triangle direct formula can be used (√3 / 4) *(side)²
Isosceles triangles having sides 6 cm , 4 cm , 4 cm
a = 6 b = 4 c = 4
s = 7
Area = √7 * 1 * 3 * 3 = 3√7 cm²
Area of 4 Such triangles = 4 * 3√7 = 12√7 cm²
= 31.749 cm²
Total Area = 10.825 + 31.749 = 42.574 cm²
50 paise per cm²
Hence cost = 42.574 * 50/100 = Rs 21.287
Woman are creative and keep house beautiful
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