Question

If ‘a’ is the side of an equilateral triangle and ‘h’ is the height, which of the following expressions can be used to find the area of the triangle?

1. $\frac{1}{2}$ $\times$ a $\times$ h

2. a $\times$ h

3. $\frac{\sqrt{3}}{4}$$a^2$

4. $\frac{\sqrt{3}}{2}$$a^2$

• A. 1 and 3
• B. 1 and 4
• C. 2 and 3
• D. 2 and 4

Answer 1

The correct option is A 1 and 3

Area of an equilateral triangle of side a is given by $\frac{\sqrt{3}}{4}$$a^2$.
We can also find area of an equilateral triangle of height h and side a as $\frac{1}{2}\times a\times h$, using the formula $\frac{1}{2}\times \text{base}\times \text{height}$.
So, both expressions 1 and 3 can be used to find the area of an equilateral triangle of side a and height h.