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A hand fan is made by stitching $10$ equal size triangular strips of two different types of paper as shown figure. The dimensions of equal strips are $25\ cm, 25\ cm$ and $14\ cm$. Find the area of each types of paper needed to make the hand fan.
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Given:
A hand fan is made by stitching $10$ equal size triangular strips of two different types of paper.
The dimensions of equal strips are $25\ cm, 25\ cm$ and $14\ cm$.
To do:
We have to find the area of each types of paper needed to make the hand fan.
Solution:
From the figure,
Area of each triangle is,
$s=\frac{a+b+c}{2}$
$=\frac{25+25+14}{2}$
$=\frac{64}{2}$
$=32$
Area of each triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{32(32-25)(32-25)(32-14)}$
$=\sqrt{32 \times 7 \times 7 \times 18}$
$=\sqrt{4 \times 4 \times 2 \times 7 \times 7 \times 2 \times 3 \times 3}$
$=4 \times 2 \times 3 \times 7$
$=168 \mathrm{~cm}^{2}$
Total area of the fan $=5 \times 168$
$=840 \mathrm{~cm}^{2}$.
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