Question

A design is made on a rectangular tile of dimensions 50 cm $\times$ 70 cm as shown in figure. The design shows 8 triangle, each of sides 26 cm, 17 cm and 25 cm. What's the total area of the design and the remaining area of the tiles.

Answer 1

Given, the dimension of rectangular tile is $50cm\times 70cm$.

$\therefore$ Area of rectangular tile
= 50 $\times$ 70 = 3500 $c{m}^2$

The sides of the design of one triangle be A = 25 cm, b = 17 cm and c = 26 cm.

Now semi-perimeter,
$s=\frac{a+b+c}{2}=\frac{25+17+26}{2}=\frac{68}{2}=34$

$\therefore$ Area of one triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
[by Heron’s formula]
$=\sqrt{34\times 9\times 17\times 8}$

$=\sqrt{17\times 2\times 3\times 3\times 17\times 2\times 2\times 2}$

$=17\times 3\times 2\times 2=204c{m}^2$

Total area of eight traingels
= 204 $\times$ 8
= 1632 $c{m}^2$

Now, area of the design
= Total area of eight triangles
$=1632c{m}^2$

Also, remaining area of the tile = Area of the rectangle – area of the design
$=3500–1632$
$=1868m^2$

Hence, the total area of the design is 1632 $c{m}^2$ and the remaining area of the tile is 1868 $c{m}^2$.