Question

Assertion: Area of an equilateral triangle having each side equal to 4 cm is $4\sqrt{3}\mathrm{sq}$ cm.
Reason: Area of an equilateral triangle having each side a is $\frac{\sqrt{3}}{4}{a}^2$ sq units.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Assertion:
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2 \\ =\frac{\sqrt{3}}{4}\times (4{)}^2 \\ =\frac{\sqrt{3}}{4}\times 16 \\ =4\sqrt{3}{\mathrm{cm}}^2 \end{gathered}$$
Reason: Area of an equilateral triangle having each side a is $\frac{\sqrt{3}}{4}{a}^2$ sq. units.
Hence, it is true.