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NCERT Solutions Class 9 Mathematics Solutions for Heron’s Formula - Exercise 12.2 in Chapter 12 - Heron’s Formula
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An umbrella is made by stitching 10 triangular pieces of cloth of two different colors (see
Fig.12.16), each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each color is
required for the umbrella?
Answer:
For each triangular piece, The semi perimeter will be
s = (50 + 50 + 20)/2 cm = 120/2 cm = 60cm
Using Heron's formula,
Area of the triangular piece = √[s (s-a) (s-b) (s-c)]
\begin{aligned} &=v[60(60-50)(60-50)(60-20)] \mathrm{cm}^{2}\\ &=\sqrt{[60 \times 10 \times 10 \times 40] \mathrm{cm}^{2}}\\ &=200 \mathrm{v} 6 \mathrm{cm}^{2}\\ &\therefore \text { The area of all the triangular pieces }=5 \times 200 \sqrt{6} \mathrm{cm}^{2}=1000 \mathrm{v} 6 \mathrm{cm}^{2} \end{aligned}
Video transcript
"hello students welcome to leader q a
video session i am seth your math tutor
and question for today is
an umbrella is made by stitching 10
triangular pieces
of cloth of two different colors see the
figure 12.16
each piece measuring 20 centimeter 50
centimeter
and 50 centimeter remember there are 10
triangular pieces of each of this
how much cloth of each color is required
for the umbrella
so we need to find how much area is
required
so here first of all let us consider the
semi parameter
semi perimeter
of each
triangle that is s
will be equal to 50 plus 50
plus 20 divided by 2
hence semi perimeter is 60 centimeter
now you can find the area for each of
this triangle piece
by using harrow's formula
so using heron's formula
area of
the triangle piece
that will be equal to root of
s s minus a s
minus b
and s minus c
so that will be equal to
root of
that is 60 60 minus 50
again 60 minus 50 and 60 minus 20.
and calculating it will give you
root of 16 into 10 into 10 into 40.
so your final answer should be 200
root 6
centimeter square and that is your area
we will indicate it with letter a so
here
i'll continue that area comes out to be
that is a 200 root
6 centimeter square
so area of all triangle pieces can be
multiplied by
multiplying the total available pieces
in the
umbrella so
so as you can see there are five
triangle pieces
so 5 into area of each piece that is 200
root 6 and that is 5 into 200 root 6
that comes out to be thousand root 6
and centimeter square
so that is our final answer if you have
any query you can drop it in our comment
section
and subscribe to lido for more such
query thank you for watching
"
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