Question

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

Answer 1

In one part of the triangle, we have $a=26cm,b=17cm$ and $c=25cm$.
Semi-perimeter of the triangle, $s=\frac{a+b+c}{2}=\frac{26cm+17cm+25cm}{2}=34cm$
Area of the triangle $=\sqrt{34\times (34-26\times (34-17)\times (34-25)}c{m}^2$
$=\sqrt{34\times 8\times 17\times 9}$

$=204{cm}^2$
So, area of the design $=8\times$ area of one triangle

$=8\times 204{cm}^2$

$=1632{cm}^2$
Now, area of the rectangular tile $=50cm\times 70cm=3500{cm}^2$
So, remaining area of tile $=$ Area of the rectangular tile $-$ Area of the design
$=3500{cm}^2-1632{cm}^2=3500{cm}^2$