the side of triangular park are 8m 10m 6m A small circular area of diameter 2m is to be left out and the remaining is to be used for growing roses how much area is used for growing roses
To determine the area used for growing roses in the triangular park, we need to calculate the area of the entire triangular park and subtract the area of the circular area that is left out.
To find the area of a triangle, we use the formula:
Area = (base * height) / 2
However, we first need to determine the height of the triangle. To do so, we can use Heron's formula to calculate its semi-perimeter and then find the height.
Heron's formula:
s = (a + b + c) / 2
where 'a', 'b', and 'c' are the lengths of the sides of the triangle.
In this case, the sides of the triangle are 8m, 10m, and 6m. Let's calculate the semi-perimeter 's':
s = (8 + 10 + 6) / 2
s = 12
Now, we can calculate the height 'h' using the formula:
h = (2 / base) * sqrt(s * (s - a) * (s - b) * (s - c))
where 'base' is the side on which we want to find the height, and 'a', 'b', and 'c' are the lengths of the other two sides.
For this calculation, let's assume the base of the triangle is 8m (as no clear indication is given in the question).
h = (2 / 8) * sqrt(12 * (12 - 10) * (12 - 6) * (12 - 8))
h = (1 / 4) * sqrt(12 * 2 * 6 * 4)
h = (1 / 4) * sqrt(576)
h = (1 / 4) * 24
h = 6
Now that we have the height of the triangle, let's calculate its area:
Area_triangle = (base * height) / 2
Area_triangle = (8 * 6) / 2
Area_triangle = 48 / 2
Area_triangle = 24 square meters
The area of the triangular park is 24 square meters.
Next, we need to determine the area of the circular space that is left out.
The diameter of the circular area is given as 2m. The formula for the area of a circle is:
Area_circle = π * radius^2
where 'π' is a mathematical constant approximately equal to 3.14159, and 'radius' is half of the diameter (1m in this case):
Area_circle = 3.14159 * (1^2)
Area_circle = 3.14159 square meters
Finally, to find the area of the park used for growing roses, we subtract the area of the circular space from the area of the triangular park:
Area_roses = Area_triangle - Area_circle
Area_roses = 24 - 3.14159
Area_roses ≈ 20.85841 square meters
Therefore, approximately 20.86 square meters of the park are used for growing roses.
you should recognize that the triangle is a right triangle of area 24
and of course, the circle has area 4π
now just finish it off.