Question

A caution sign is shown in the given figure. Find the area to be painted in red (shaded in figure), in order to warn the people about the danger ahead. [Use $\sqrt{3}=1.732$]

• A. $443.4c{m}^2$
• B. $440.4c{m}^2$
• C. $438.4c{m}^2$
• D. $449.4c{m}^2$

Answer 1

The correct option is A $443.4c{m}^2$

Area of equilateral triangle with side a is given by:
$\frac{\sqrt{3}}{4}{a}^2$
Area of larger triangle $=\frac{\sqrt{3}}{4}(40{)}^2$
Area of smaller triangle $=\frac{\sqrt{3}}{4}(24{)}^2$
$\Rightarrow Requiredarea=\frac{\sqrt{3}}{4}(40{)}^2-\frac{\sqrt{3}}{4}(24{)}^2$
$=\frac{\sqrt{3}}{4}(1600-576)$
$=\frac{\left(1.732\right)}{4}\times 1024=443.4c{m}^2$