An umbrella is made by stitching 10 pieces of cloth of two different colours, each piece measuring

20cm,50cm,50cm
. ____ is the area of cloth of each colour is required for an umbrella?

Question

An umbrella is made by stitching 10 pieces of cloth of two different colours, each piece measuring

20cm,50cm,50cm
   . ____ is the area of  cloth of each colour is required for an umbrella?

Accepted Answer

It is given that an umbrella is made of 10 triangular pieces of two different colors.Suppose the given two colors are green and white.So we can say that there are 5 triangular pieces of green color and 5 pieces of white color.Let's take one triangle and draw the height as shown below.We are given that the dimensions of each triangle are

20cm,50cm,50cm
  .So, from the triangle

ΔABC
   we have

⇒AB=AC=50cm

⇒BC=20cm

We know that the height of an isosceles triangle will be the medianSo point "D" is midpoint of point "BC"So we can length “DC” as

⇒DC=
      
       BC
      2

⇒DC=
      
       20
      2
     
     cm=10cm

The Pythagoras theorem is given as

b
    2
   
   =
    a
    2
   
   +
    c
    2

.By using the above theorem to triangle

ΔADC
   we get

⇒A
    D
    2
   
   +D
    C
    2
   
   =A
    C
    2

⇒A
      D
      2
     
     +
      10
      2
     
     =
      50
      2

⇒A
      D
      2
     
     =2500−100

⇒AD=
      
       2400
     
     =20
      6
     
     cm

Area formula of triangle,

A=
    1
    2
   
   (Base)(Height)
  Let us assume that the area of triangle

ΔABC
   as

a
  ,Then by using the area formula we get

⇒a=
    1
    2
   
   (BC)(DC)
  Now, by substituting the required values in above equation we get’

⇒a=12(20cm)(20
      6
     
     cm)

⇒a=200
      6
     
     c
      m
      2

We are given that there are 5 triangular pieces of each suit.So the total fabric of each color is obtained by multiplying the area of ​​each triangle by 5Suppose the fabric required for each color as

A
   then we get,

⇒A=a×5

⇒A=200
      6
     
     ×5

⇒A=1000
      6

Therefore it requires

1000
    6
   
   c
    m
    2

of cloth of each colour is required for the given umbrella.

An umbrella is made by stitching 10 pieces of cloth of two different colours, each piece measuring $20 c m, 50 c m, 50 c m$ . ____ is the area of cloth of each colour is required for an umbrella?

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An umbrella is made by stitching 10 pieces of cloth of two different colours, each piece measuring 20cm,50cm,50cm . ____ is the area of cloth of each colour is required for an umbrella?