Question

Suman made an arrangement with white and black coloured paper sheets as shown in figure. The total areas of the white and black paper sheets used in making the arrangement is $15c{m}^2$.

• A. True
• B. False

Answer 1

The correct option is B False

Given: dimension of a black triangular sheet is: $2cm,2cm,1.5cm$
We have semi-perimeter of the triangle, $s=\frac{2+2+1.5}{2}=2.75cm$
Now, area of a black triangular sheet $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{2.75(2.75-2)(2.75-2)(2.75-1.5)}=\sqrt{2.75\times 0.75\times 0.75\times 1.25}=1.39{cm}^2$
So, area of black paper sheets used $=4\times$ Area of 1 black triangular sheet

$=4\times 1.39=5.56{cm}^2$

Dimensions of bigger triangular paper sheet are: $4cm,4cm,3cm$.

So, semi-perimeter of the triangle, $s=\frac{a+b+c}{2}=\frac{4+4+3}{2}=5.5cm$
Area of a bigger triangular sheet $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{5.5(5.5-4)(5.5-4)(5.5-3)}$

$=\sqrt{5.5\times 1.5\times 1.5\times 2.5}$

$=5.56{cm}^2$
So, Area of 4 bigger triangular sheet $=4\times 5.56=22.24{cm}^2$
Therefore, area of white paper sheet used in 4 white triangular design

$=$ Area of 4 bigger triangular sheets $-$ Area of 4 black paper sheets used

$=22.24{cm}^2-5.56{cm}^2$

$=16.68{cm}^2$