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  • A design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in Figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.

A design is made on a rectangular tile of dimensions $50 \mathrm{~cm} \times 70 \mathrm{~cm}$ as shown in Figure. The design shows 8 triangles, each of the sides $26 \mathrm{~cm}, 17 \mathrm{~cm}$ and 25 cm. Find the total area of the design and the remaining area of the tile.

Answers (1)

Solution.

We have the dimensions of the rectangle tile as $50 \mathrm{~cm} \times 70 \mathrm{~cm}$

We know that area of a rectangle $=$ length $\times$ breadth

Area of tile $=(70 \times 50) \mathrm{cm}^2=3500 \mathrm{~cm}^2$

Given sides of triangular design: $26 \mathrm{~cm}, 17 \mathrm{~cm}, 25 \mathrm{~cm}$

To find the area using Heron's formula

Let, $\mathrm{a}=26 \mathrm{~cm}, \mathrm{~b}=17 \mathrm{~cm}, \mathrm{c}=25 \mathrm{~cm}$

$
S=\frac{a+b+c}{2}=\frac{26+17+25}{2}=\frac{68}{2}=34 \mathrm{~cm}
$

$
\begin{aligned}
& \text { Area of triangle }=\sqrt{S(S-a)(S-b)(S-c)} \\
& =\sqrt{34(34-26)(34-17)(34-25)} \\
& =\sqrt{34 \times 8 \times 17 \times 9} \\
& =\sqrt{17 \times 2 \times 2 \times 2 \times 2 \times 17 \times 3 \times 3} \\
& =2 \times 2 \times 3 \times 17
\end{aligned}
$

Area of $\triangle \mathrm{ABC}=204 \mathrm{~cm}^2$

But we have 8 triangles of equal area.

So the area of design $=8 \times$ area of one $\Delta$

$
=8 \times 204=1632 \mathrm{~cm}^2
$

The remaining area of tile $=$ Area of tile - Area of design

$
=(3500-1632) \mathrm{cm}^2=1868 \mathrm{~cm}^2
$

Hence the area of the design is $1632 \mathrm{~cm}^2$ and the remaining area of the tile is $1868 \mathrm{~cm}^2$.

 

Posted by

infoexpert21

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