Question

The height of an equilateral triangle is 5 cm. Find its area.​

Answer 1

Ответ:

25/√3 см²

Объяснение:

Высота равностороннего треугольника равна 5. Найти его площадь.

h=a√3/2, a- сторона треугольника.

а=2*h/√3=2*5/√3=10/√3 см сторона треугольника.

S=a²√3/4=(10/√3)²*√3:4=100/√3*1/4

=25/√3 см²

Answer 2

To find the area of an equilateral triangle, you can use the following formula:

Area = (sqrt(3) / 4) * side^2

In this case, you are given the height of the equilateral triangle, which is 5 cm. To find the side length (denoted as "side"), you can use the following relationship:

side = 2 * (height / sqrt(3))

Plugging in the given height:

side = 2 * (5 cm / sqrt(3))

Now, calculate the side length:

side = 10 cm / sqrt(3)

To simplify the expression, multiply both the numerator and denominator by sqrt(3):

side = (10 cm * sqrt(3)) / (sqrt(3) * sqrt(3)) side = (10 cm * sqrt(3)) / 3

Now that you have the side length, you can find the area of the equilateral triangle:

Area = (sqrt(3) / 4) * side^2 Area = (sqrt(3) / 4) * [(10 cm * sqrt(3)) / 3]^2

Now, calculate the area:

Area = (sqrt(3) / 4) * [(10 cm * sqrt(3))^2 / 3^2] Area = (sqrt(3) / 4) * [(300 cm^2) / 9]

Now, simplify further:

Area = (sqrt(3) / 4) * (100 cm^2) Area = (sqrt(3) * 100 cm^2) / 4 Area = (100 sqrt(3) cm^2) / 4 Area = 25 sqrt(3) cm^2

So, the area of the equilateral triangle is 25√3 square centimeters.