Question

Question 8
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. find 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 $c{m}^2$.