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Question 8
A design is made on a rectangular tile of dimensions 50 cm × 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.


Solution

Given, the dimension of rectangular tile is
50 cm× 70 cm.
Area of rectangular tile = 50 × 70 = 3500 cm2
The sides of the design of one triangle be
 A = 25 cm, b = 17 cm and c = 26 cm.
Now semi-perimeter,
s=a+b+c2=25+17+262=682=34
  Area of one triangle =s(sa)(sb)(sc) [by Heron’s formula]
=34×9×17×8
=17×2×3×3×17×2×2×2
=17×3×2×2=204 cm2
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.

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