the area of an equilateral triangle is given by the expression s^2 x square root of 3/4, where s is the side length of the triangle. what is the area of the triangle? round to the nearest tenth
the triangle is 5 cm on all three sides.
A = 0.5*AB*AC*sin A=0.5 *5 * 5 * sin 60 = 10.8 cm^2.
To find the area of an equilateral triangle, you can use the formula:
Area = s^2 * √3 / 4
Given that the side length (s) of the equilateral triangle is 5 cm, we can substitute that value into the formula:
Area = (5 cm)^2 * √3 / 4
= 25 cm^2 * (√3 / 4)
Now, let's calculate the value of (√3 / 4):
√3 ≈ 1.732
√3 / 4 ≈ 1.732 / 4
≈ 0.433
To find the area, we multiply (25 cm^2) by 0.433:
Area ≈ 25 cm^2 * 0.433
≈ 10.825 cm^2
Rounded to the nearest tenth, the area of the equilateral triangle is approximately 10.8 cm^2.
To find the area of an equilateral triangle, we can use the formula provided:
Area = s^2 * √3/4
Let's substitute the given side length, s = 5 cm, into the formula:
Area = (5 cm)^2 * √3/4
First, let's calculate the square of the side length:
(5 cm)^2 = 25 cm^2
Now, let's substitute this value back into the formula:
Area = 25 cm^2 * √3/4
Next, let's simplify the expression √3/4:
√3/4 ≈ 0.866
Now, multiply the simplified value by the square of the side length:
Area ≈ 25 cm^2 * 0.866
To find the rounded answer to the nearest tenth, we multiply the two values:
Area ≈ 21.65 cm^2
Therefore, the area of the equilateral triangle, rounded to the nearest tenth, is approximately 21.7 cm^2.