MCQ
The height of an equilateral triangle is $6\ cm.$ Its area:
- ✓$12\sqrt{3}\text{cm}^2$
- B$6\sqrt{3}\text{cm}^2$
- C$12\sqrt{2}\text{cm}^2$
- D$18\text{cm}^2$
✓
Answer
Correct option: A.
$12\sqrt{3}\text{cm}^2$
Height of equilateral triangle $=\frac{\sqrt{3}}{2}\times\text{Side}$
$\Rightarrow6=\frac{\sqrt{3}}{2}\times\text{Side}$
$\Rightarrow\text{Side}=\frac{12}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{12}{3}\times\sqrt{3}=4\sqrt{3}\text{cm}$
Now,
Area of equilateral triangle $=\frac{\sqrt{3}}{2}\times(\text{Side})^2$
$=\frac{\sqrt{3}}{4}\times(4\sqrt{3})^2$
$=\frac{\sqrt{3}}{4}\times48$
$=12\sqrt{3}\text{cm}^2$
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