Question

"Question 6 An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

Class 9 - Math - Heron's Formula Page 207"

Answer 1

Hello

Here is your answer.

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Solution:-
_______

For pieces of triangle,

a = 20 cm , b = 50 cm , c = 50 cm

.°. s = a + b + c / 2

= 20 + 50 + 50 / 2

= 120 / 2

= 60 cm

.°. a triangles area = √ s ( s - a ) ( s - b ) ( s - c )

= √ 60 ( 60 - 20 ) ( 60 - 50 ) ( 60 - 50 )

= √ 60 ( 40 ) ( 10 ) ( 10 )

= 200√6 cm²

.°. one colour of five triangles area ,

= 5 ( 200√6 ) cm²

= 1000√6 cm²

so, there are 1000√6 cm² cloth of each colour is required for the umbrella.

thanks

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Answer 2

There are 10 triangles, out of which 5 of black and 5 of grey color. Now,

Area of of each cloth=5× area of 1 triangle

Area of triangle=

s(s−a)(s−b)(s−c)

,s=

2

a+b+c

=

2

50+20+50

s=60㎝

∴ar△=

60(60−50)(60−20)(60−50)

=

60×10×40×10

=

6×10×10×4×10×10

=2×10×10

6

=200

6

㎠

Area of each cloth required=(5×200

6

)㎠=1000

6

㎠

Hope it help