MCQ
The height of an equilateral triangle is $\sqrt{6}\text{cm}.$ Its area is:
- A$3\sqrt{3}\text{cm}^2$
- ✓$2\sqrt{3}\text{cm}^2$
- C$2\sqrt{2}\text{cm}^2$
- D$6\sqrt{2}\text{cm}^2$
✓
Answer
Correct option: B.
$2\sqrt{3}\text{cm}^2$
Let a be the side of an equilateral triangle
$\therefore\text{Altitude}=\frac{\sqrt{3}}{2}\text{a}$
$\therefore\frac{\sqrt{3}}2{}\text{a}=\sqrt{6}$
$\Rightarrow\text{a}=\frac{\sqrt{6}\times2}{\sqrt{3}}=2\sqrt{2}$
and area $=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}(2\sqrt{2})^2$
$=\frac{\sqrt{3}}4{}\times4\times2$
$=2\sqrt{3}\text{cm}^2$
$\therefore\text{Altitude}=\frac{\sqrt{3}}{2}\text{a}$
$\therefore\frac{\sqrt{3}}2{}\text{a}=\sqrt{6}$
$\Rightarrow\text{a}=\frac{\sqrt{6}\times2}{\sqrt{3}}=2\sqrt{2}$
and area $=\frac{\sqrt{3}}{4}\text{a}^2=\frac{\sqrt{3}}{4}(2\sqrt{2})^2$
$=\frac{\sqrt{3}}4{}\times4\times2$
$=2\sqrt{3}\text{cm}^2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The per cent that represents the shaded region in the figure is:
On selling an article for $Rs. 144$ a man loses $10\%$. At what price should he sell it to gain $10\%?$
→The area of the parallelogram $A B C D$ in which $A B=6.2 cm$ and the perpendicular from $C$ on $A B$ is 5 cm , is
→Mark $(\checkmark)$ against the correct answer in the following: $-2\frac{1}{9}-6=?$
→Tick $(\checkmark)$ the correct answer.
A scalene triangle has:
→A scalene triangle has:
In the number $0.257,$ which of the following does the digit $7$ represent$?$
→What distance (in m) will a train cover in 1 minute travelling at $72\frac{\text{km}}{\text{h}}$?
→What do you call solid figures with line segments as their edges?
State $T$ for true and $F$ for false.
$(i).$ Every rational number can be expressed with a positive numerator.
$(ii). \frac{3}{11}$ cannot be represented as a non$-$terminating repeating decimal.
$(iii).$ If $ \frac{\text{p}}{\text{q}}$ and $\frac{\text{r}}{\text{s}}$ are two terminating decimals, then $ \frac{\text{p}}{\text{q}}\times\frac{\text{r}}{\text{s}}$ is also a terminating decimal.
$(iv).$ If $\frac{\text{p}}{\text{q}}$ is non$-$terminating repeating decimal and $\frac{\text{r}}{\text{s}}$ is a terminating decimal, then $\Big(\frac{\text{p}}{\text{q}}\div\frac{\text{r}}{\text{s}}\Big)$ is a terminating decimal.
→$(i).$ Every rational number can be expressed with a positive numerator.
$(ii). \frac{3}{11}$ cannot be represented as a non$-$terminating repeating decimal.
$(iii).$ If $ \frac{\text{p}}{\text{q}}$ and $\frac{\text{r}}{\text{s}}$ are two terminating decimals, then $ \frac{\text{p}}{\text{q}}\times\frac{\text{r}}{\text{s}}$ is also a terminating decimal.
$(iv).$ If $\frac{\text{p}}{\text{q}}$ is non$-$terminating repeating decimal and $\frac{\text{r}}{\text{s}}$ is a terminating decimal, then $\Big(\frac{\text{p}}{\text{q}}\div\frac{\text{r}}{\text{s}}\Big)$ is a terminating decimal.
Mark against the correct answer in the following: If $5\text{x}-\frac{3}{4}=2\text{x}-\frac{2}{3}$ then $x =?$
→