Find the area of an equilateral triangle with an apothem of 6 cm? Round your answer to the nearest tenth.
To find the area of an equilateral triangle, we need to know either the length of one of its sides or the length of the apothem. Since we are given the apothem, we can use it to find the side length.
An apothem is the perpendicular distance from the center of an equilateral triangle to one of its sides. In an equilateral triangle, the apothem is also the height of the triangle.
To find the side length, we can use the formula for an equilateral triangle:
Side length = 2 * (apothem / √3)
Substituting the given value:
Side length = 2 * (6 cm / √3)
Side length ≈ 2 * (6 cm / 1.732)
Side length ≈ 6.9282 cm (rounded to the nearest tenth)
Now that we know the side length, we can use it to find the area of the equilateral triangle.
Area = (√3 / 4) * (side length)^2
Substituting the value of the side length:
Area = (√3 / 4) * (6.9282 cm)^2
Area ≈ (√3 / 4) * (47.996 cm^2)
Area ≈ 20.784 cm^2 (rounded to the nearest tenth)
Therefore, the area of the equilateral triangle with an apothem of 6 cm is approximately 20.8 square centimeters.
the sides of a 30-60-90 right triangle are in the ratio 1:√3:2
so the base of the triangle has length 2*6/√3 = 4√3
That makes the area of the triangle
1/2 bh = 1/2 * 4√3 * 6 = 12√3