The area of an equilateral triangle can be calculated using the formula: Area = (1/2) * apothem * perimeter
Since the triangle is equilateral, all three sides are equal. Let's denote the side length as x.
The perimeter of the triangle is 3x, and since the apothem is 7 cm, we can use the Pythagorean theorem to find the side length:
(7)^2 + (x/2)^2 = x^2
49 + x^2/4 = x^2
49 = 3x^2/4
196 = 3x^2
x^2 = 196/3
x = √(196/3)
x ≈ 7.54 cm
Now we can find the perimeter = 3x ≈ 22.62 cm
Finally, we can calculate the area:
Area = (1/2) * 7 cm * 22.62 cm ≈ 79.17 cm^2
Rounded to the nearest whole number, the area is 79 cm^2.
Therefore, none of the provided options are correct.
Find the area of an equilateral triangle with apothem 7 cm. Round to the nearest whole number.
170 cm2
255 cm2
130 cm2
85 cm2
1 answer