Question

Construct an equilateral triangle whose altitude is $5$ $cm$. Then, area of the required triangle is:

• A. $13.6c{m}^2$
• B. $14.5c{m}^2$
• C. $12.8c{m}^2$
• D. $11.2c{m}^2$

Answer 1

Answer: (B)

$14.5c{m}^2$

We know that in an equilateral triangle, all angles are equal to $={60}^0$ and the altitude bisects the opposite angle.
Hence, follow the steps given below to construct the triangle.
1. Draw a line $PQ$ and mark a point $D$ on it.
2. Construct a perpendicular of length $DA=5cm$ to $PQ$ at point $D$
3. Construct $\angle DAR=\frac{{60}^0}{2}={30}^0$ to intersect $PQ$ at $B$
4. Measure $BD$ and cut off an arc on $PQ$ of same distance $DC$ on the other side of $D$
5. Join $A$ to $C$
6. $ABC$ is the required equilateral triangle.

On measuring the length of the sides, we get side length as $5.8cm$

$\therefore$ Area of triangle $=\frac{1}{2}\times 5.8\times 5=14.5c{m}^2$