ABC26GN4482 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The height of an equilateral triangle is 10 cm. Its area is
(a)$\frac{100}{3} \mathrm{cm}^{2}$
(b)$30 \mathrm{cm}^{2}$
(c)$100 \mathrm{cm}^{2}$
(d)$\frac{100}{\sqrt{3}} \mathrm{cm}^{2}$
Answer
Explanation
Let each side be $a \mathrm{cm}$. Then, $$\begin{aligned} \left(\frac{a}{2}\right)^{2}+(10)^{2}=a^{2} & \Leftrightarrow\left(a^{2}-\frac{a^{2}}{4}\right)=100 \\ & \Leftrightarrow \frac{3 a^{2}}{4}=100 \Leftrightarrow a^{2}=\frac{400}{3} . \\ \therefore \text { Area }=\frac{\sqrt{3}}{4} \times a^{2} & =\left(\frac{\sqrt{3}}{4} \times \frac{400}{3}\right) \mathrm{cm}^{2}=\frac{100}{\sqrt{3}} \mathrm{cm}^{2} . \end{aligned}$$
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