Answer:
[tex]21.7\text{ cm}^2[/tex]
Step-by-step explanation:
We have been given an image of a 30-60-90 triangle. We are asked to find the area of our given triangle.
[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Base}\times\text{Height})[/tex]
First of all, we need to find the height of our given triangle.
In a 30-60-90 triangle, the shorter leg that corresponds to 30 degree angle is [tex]x[/tex] units long. The sides corresponding to 60 and 90 degree angles are [tex]x\sqrt{3}[/tex] and [tex]2x[/tex] respectively.
Since the value of [tex]x[/tex] is 5 cm, so the height of our given triangle (corresponding to 60 degree angle) will be:
[tex]x\sqrt{3}=5\sqrt{3}[/tex]
Upon substituting our given values in area of triangle formula we will get,
[tex]\text{Area of triangle}=\frac{1}{2}\times (5\times 5\sqrt{3})[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times (25\sqrt{3})[/tex]
[tex]\text{Area of triangle}=12.5\sqrt{3}[/tex]
[tex]\text{Area of triangle}=21.65063509\approx 21.7[/tex]
Therefore, the area of our given triangle is 21.7 square centimeters.
