Question Detail
The height of an equilateral triangle is 10 cm. find its area.
- \begin{aligned} \frac{120}{\sqrt{3}} cm^2 \end{aligned}
- \begin{aligned} \frac{110}{\sqrt{3}} cm^2 \end{aligned}
- \begin{aligned} \frac{100}{\sqrt{3}} cm^2 \end{aligned}
- \begin{aligned} \frac{90}{\sqrt{3}} cm^2 \end{aligned}
Answer: Option C
Explanation:
Let each side be a cm, then
\begin{aligned}
\left(\frac{a}{2}\right)^2+{10}^2 = a^2 \\
<=>\left(a^2-\frac{a^2}{4}\right) = 100 \\
<=> \frac{3a^2}{4} = 100 \\
a^2 = \frac{400}{3} \\
Area = \frac{\sqrt{3}}{4}*a^2 \\
= \left(\frac{\sqrt{3}}{4}*\frac{400}{3}\right)cm^2 \\
= \frac{100}{\sqrt{3}}cm^2
\end{aligned}