Question

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

Answer 1

Given, the dimension of rectangular tile is 50 cm × 70 cm.

∴ Area of rectangular tile = 50 × 70 = 3500 cm²

The sides of a design of one triangle be

a = 25 cm, b = 17 cm and c = 26 cm

Now, semi-perimeter,

`s = (a + b + c)/2`

= `(25 + 17 + 26)/2`

= `68/2`

= 34

∴  Area of one triangle = `sqrt(s(s - a)(s - b)(s - c))`  ...[By Heron’s formula]

= `sqrt(34 xx 9 xx 17 xx 8)`

= `sqrt(17 xx 2 xx 3 xx 3 xx 17 xx 2 xx 2 xx 2)`

= 17 × 3 × 2 × 2

= 204 cm²

∴ Total area of eight triangles = 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 cm²

Hence, the total area of the design is 1632 cm² and the remaining area of the tile is 1868 cm².