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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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Updated on: 10-Oct-2022

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