Given, the dimension of rectangular tile is 50cm × 70cm.
∴ Area of rectangular tile = 50 × 70 = 3500 cm2
The sides of the design of one triangle be
A = 25cm, b = 17cm and c = 26cm.
Now semi-perimeter, s=a+b+c2=25+17+262=682=34
∴ Area of one triangle =√s(s−a)(s−b)(s−c) [by Heron’s formula]
=√34×9×17×8
=√17×2×3×3×17×2×2×2
=17×3×2×2=204cm2
Total area of eight traingels = 204 × 8 = 1632 cm2
now, area of the design = Total area of eight triangles
=1632 cm2
Also, remaining area of the tile = Area of the rectangle – area of the design
= 3500 – 1632
=1868 m2
Hence, the total area of the design is 1632 cm2 and the remaining area of the tile is 1868 cm2.