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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(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=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.  Suggest corrections  Similar questions
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