Question

There are two identical circles with same inside design as shown in the figure. The identical triangular leaves are to be painted red and the remaining area green. Find the total area to be painted red.

• A. $1512c{m}^2$
• B. $1162c{m}^2$
• C. $1632c{m}^2$
• D. $1521c{m}^2$

Answer 1

The correct option is A $1512c{m}^2$

Area of one triangular leaf
$=\sqrt{s(s-a)(s-b)(s-c)}$
$s=\frac{41+28+15}{2}=\frac{84}{2}=42$
Area of a triangle
$=\sqrt{42(42-41)(42-28)(42-15)}$
$=\sqrt{42\times 1\times 14\times 27}$
$=126c{m}^2$
Area of six triangular leaves
$=126\times 6$
$=756c{m}^2$
Since two such circles are there,
Total area to be painted red $=756\times 2=1512c{m}^2$