Question
A design is made on a rectangular tile of dimensions 50cm × 70cm as shown in 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
Given, tha dimension of rectangular lile is 50cm × 70cm
Area of rectangular tile = 50 × 70 = 3500cm2
The sides of a design of one triangle be,
a = 25cm, b = 17cm and c = 26cm
Now, semi-perimeter, $\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}=\frac{25+17+26}{2}=\frac{68}{2}=34$
$\therefore$ Area of one triangle $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$ [by Heron's formula]
$=\sqrt{34\times9\times17\times8}$
$=\sqrt{17\times2\times3\times3\times17\times2\times2\times2}$
$=17\times3\times2\times2=204\text{cm}^2$
$\therefore$ Total area of eight triangles = 204 × 8 = 1632cm
Now, area of the desion = Total area of eight triangles
= 1632cm2
Also, remaining area of the tile = Area of the rectangle - Area of the design
= 3500 - 1632
= 1868cm
Hence, the total area of the design is 1632cm2 and the remaining area of the tile is 1868cm2
Area of rectangular tile = 50 × 70 = 3500cm2
The sides of a design of one triangle be,
a = 25cm, b = 17cm and c = 26cm
Now, semi-perimeter, $\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}=\frac{25+17+26}{2}=\frac{68}{2}=34$
$\therefore$ Area of one triangle $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$ [by Heron's formula]
$=\sqrt{34\times9\times17\times8}$
$=\sqrt{17\times2\times3\times3\times17\times2\times2\times2}$
$=17\times3\times2\times2=204\text{cm}^2$
$\therefore$ Total area of eight triangles = 204 × 8 = 1632cm
Now, area of the desion = Total area of eight triangles
= 1632cm2
Also, remaining area of the tile = Area of the rectangle - Area of the design
= 3500 - 1632
= 1868cm
Hence, the total area of the design is 1632cm2 and the remaining area of the tile is 1868cm2
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