Question

Find the area of the equilateral triangle having length of each side 50 cm.

Answer 1

Hint : In this problem, we have to find the area of the equilateral triangle whose side is given. We know that for an equilateral triangle with a side, we can find the area. We know that the area of an equilateral triangle is \[\dfrac{\sqrt{3}}{4}{{a}^{2}}\] , where a is the side of the triangle. We can now substitute the value of the side given in this formula and simplify it to get the value of the area of the equilateral triangle.

Complete step-by-step solution:
We know that the given side of the equilateral triangle is 50cm.

We know that the area of the equilateral triangle is,
Area of the equilateral triangle = \[\dfrac{\sqrt{3}}{4}{{a}^{2}}\]……. (1)
 We know that, we are given
\[a=50\]
We can substitute the above value in the area of the equilateral triangle formula (1),
Area of the equilateral triangle = \[\dfrac{\sqrt{3}}{4}\times {{\left( 50 \right)}^{2}}=\dfrac{\sqrt{3}\times 2500}{4}=625\sqrt{3}\]sq.cm.
Therefore, the area of an equilateral triangle with the side 50cm is \[625\sqrt{3}\] sq.cm.

Note:We should always remember some formulas in geometry, such as area or area of the equilateral triangle. We should remember that the area of the equilateral triangle is \[\dfrac{\sqrt{3}}{4}{{a}^{2}}\], where a is the sides of the equilateral triangle. An equilateral triangle is one, in which all the sides will be equal. We can also write the exact value of the area by substituting the square root value and multiplying it.